VIABILITY AND CHARACTERIZATION OF A PLASMA WINDOW AS A FLOW

LIMITER FOR AN ION BEAM GAS CHARGE STRIPPER

By

Andrew Leo LaJoie

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics—Doctor of Philosophy

2020

ABSTRACT

VIABILITY AND CHARACTERIZATION OF A PLASMA WINDOW AS A FLOW

LIMITER FOR AN ION BEAM GAS CHARGE STRIPPER

By

Andrew Leo LaJoie

Charge stripping is an increasingly necessary process in ion accelerators, particularly

those which are used in accelerating high mass nuclei such as uranium. Generally in ac-

celerator facilities, heavy ions are produced in the ion source with a relatively low charge

state distribution. In the charge stripper, further removal of electrons from the ion beam

enables greater energy gain in accelerating cavities downstream of the charge stripper, which

can lower cost of attaining a desired energy. For this reason the charge stripper is typically

located early in the accelerator. The ion acceleration community is met with an increas-

ingly strong demand for higher particle counts in the ion beams because facility users almost

always can benefit from higher statistics in their experiments. This means higher beam

intensities. This need for higher intensity presents the challenge of preventing traditionally

employed solid charge strippers, like diamond-like carbon (DLC) foils, from suffering over-

whelming kinetic impact damage from the beam and reducing or eliminating their charge

stripping function. These issues are even more critical when stripping heavy ions because

of their much larger energy deposition per unit length compared with protons or low mass

heavy ions. This high energy deposition results from a sharper Bragg peak for heavier ions.

Alternatively, gas charge strippers do not suffer from this kind of irreparable degradation,

but do present a host of other unique challenges. Chief among these challenges is confining

the gas to only a small segment of the beamline and preventing it from excessively leaking

to other upstream and downstream components of the beamline whose performance can

be hindered or entirely prevented by pressures above 10-7 torr. The plasma window (PW)

device is one which can limit the flow of gas from a high pressure gas charge stripping

chamber (GCS) to the surrounding low pressure beamline - without the need for any solid

interface, that would likely be damaged or destroyed by the ion beam. The PW is a direct

current (DC) cascaded arc which heats and ionizes the gas flowing out of the GCS, thereby

restricting the flow by greatly reducing the density of the gas flow. One would be located

on both ends of the GCS. The degree to which this limits the gas flow depends on the

temperature attained within the arc, which primarily depends upon the pressure maintained

in the GCS and the arc current. These parameters are the operating conditions which can be

user-controlled in a fixed-geometry PW to tune its utility. In addition, the PW performance

depends on its geometry, both its channel radius and channel length. Both helium and argon

are studied, each having pros and cons for potential gas charge stripper applications which

will be summarized. Within the operating conditions and geometry studied in this thesis,

the PW can reduce the gas flow escaping from the GCS by a factor of up to about 24 in

argon and 15 in helium.

The goal of the work summarized in this thesis was to quantify the utility of the PW

in reducing the gas leakage rate from the gas charge stripper in a variety of operating

conditions, and to gain an understanding of the mechanisms involved in effecting the flow

rate reduction. Design recommendations for a next generation PW are also given to address

persisting challenges with employing it in tandem with a GCS for ion beams. This work

shows that a PW-based gas charge stripper system may be effective for future high intensity

ion accelerators. To get to that point, more work is necessary to extend the continuous,

uninterrupted lifetime of the plasma window.

ACKNOWLEDGMENTS

There are a great many individuals without whose support this thesis would not be what

it is now. Firstly thank you to Ady Hershcovitch and Peter Thieberger at Brookhaven

National Laboratory for providing much of the components of the original plasma window

used for this project, as well as insights into how to initiate and maintain the arc.

Thank you to my research advisor Felix Marti for your experience, patience, and encour-

agement throughout this project, helping to bring it from a device whose physical mechanisms

for performance were rather nebulous and hidden to something that we now have a much

better understanding of. I also thank Jian Gao for his contributions towards that same goal,

especially in providing assistance in bringing the performance of the plasma window to bear.

Thank you to Steve Lund for serving as my guidance committee chair and academic advi-

sor, for providing valuable input and insights into improving publication and presentation

quality, and for helping guide me towards promising employment prospects. I would also

like to thank my other guidance committee members, John Verboncoeur, Tim Grotjohn, and

Chong-Yu Ruan for their suggestions and constructive comments throughout my graduate

career.

I also would like to thank the numerous friends - fellow graduate students I met at

Michigan State University, as well as those I met earlier as an undergraduate - who’ve

provided encouragement and support throughout my time at Michigan State University.

Whether it was watching movies, playing games, sharing drinks, or just having conversations,

I’m glad that you’ve been a part of my graduate school experience - the best part, in

fact. Daine Smith, Brittany Lindstrom, Rachel Holt, Terri Poxon-Pearson, Roy Ready, Lisa

Carpenter, Brandon Elman, Alice Mills, Bryan Isherwood and so many others that I regret

iv

not being able to take up an entire page mentioning, you have all made the graduate school

experience infinitely more endurable. My family members have also been a constant source

of support, and I am incredibly grateful to you all!

Finally, I owe a huge thank you to my wife-to-be Nicki Larson. Your continuous encour-

agement has kept me going through even the toughest times, and you have helped pull me

back to real life when I’d been spending too much time with my head buried in the world

of the plasma window. You and Mars (our cat) have been great at providing much-needed

distractions from work when it became overwhelming (or in the case of Mars, whenever he

felt like it). Thank you so much for everything, you are the best!

v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

KEY TO ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Charge Stripping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Cascaded Arc Discharge . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Collisions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Equilibrium Types
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Spectrometer Characteristics

Chapter 2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Test Stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Plasma Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Diagnostics
. . . . . . . . . . . . . . . . .
2.1.3.1
2.1.3.2 Coolant Calorimetry . . . . . . . . . . . . . . . . . . . . . .
2.1.3.3 Plate Floating Voltages
. . . . . . . . . . . . . . . . . . . .
2.2 Optical Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Electron Density - Stark Broadening . . . . . . . . . . . . . . . . . .
2.2.3 Electron Temperature
. . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3.1 Applicability of Partial Local Thermodynamic Equilibrium .
2.2.4 Radiation Reabsorption . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Cathode Longevity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
11
12
20
21
25
26

28
28
31
36
43
43
45
47
48
48
53
69
73
77
79

Chapter 3 Background and Models . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Electron Energy Distribution Function . . . . . . . . . . . . . . . . . . . . .
3.2 Collisional-Radiative Model (HeCRM)
3.3

92
92
. . . . . . . . . . . . . . . . . . . . . 101
1D Model
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3.1 Overall Momentum Balance . . . . . . . . . . . . . . . . . . . . . . . 108
3.4 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.5 Plasma Simulation Model - PLASIMO . . . . . . . . . . . . . . . . . . . . . 122
3.6 Effect of Plasma Window on Ion Beam . . . . . . . . . . . . . . . . . . . . . 136

vi

Chapter 4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.1 Flow Rates in Plasma Window Configurations . . . . . . . . . . . . . . . . . 142
4.2 Single-Aperture Plasma Window Results . . . . . . . . . . . . . . . . . . . . 146
4.2.1 PLASIMO Comparison Method . . . . . . . . . . . . . . . . . . . . . 147
4.2.2 Electron Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.2.3 Electron Temperature
. . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.2.4 Electric Field and DC Conductivity . . . . . . . . . . . . . . . . . . . 163
4.2.5 Component Heat Depositions
. . . . . . . . . . . . . . . . . . . . . . 170
4.2.6 Contributions to Flow Rate Reduction . . . . . . . . . . . . . . . . . 173
4.3 Two-Aperture Plasma Window Results . . . . . . . . . . . . . . . . . . . . . 185
4.4 Lessons Learned and Potential Improvements
. . . . . . . . . . . . . . . . . 188
4.4.1 Cathode Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
4.4.2 Plasma Window Structure . . . . . . . . . . . . . . . . . . . . . . . . 191
4.4.3 Recirculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
4.4.4 Plasma Window Performance Summary . . . . . . . . . . . . . . . . 200
4.4.5 Charge Stripper Gas Species Choice . . . . . . . . . . . . . . . . . . . 202
4.5 Empirical Scaling Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Chapter 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

vii

LIST OF TABLES

Table 2.1:

Comparison of electron-impact ionization rates from ground and metastable
levels in Ar and He. All rate coefficients are in [m3/s]. . . . . . . . .
53

Table 2.2:

Approximate relative line broadening degrees (∆λ/λ) for various mech-
anisms, for emissions in visible wavelengths. In argon, Te ≈ 1.5 eV,
Tg ≈ 1.5 eV, and ne ≈ 2 × 1016 cm-3.
In helium, Te ≈ 2.5 eV,
Tg ≈ 1.5 eV, and ne ≈ 2 × 1015 cm-3.
. . . . . . . . . . . . . . . . .

56

Table 2.3:

Selected Ar II emission properties for lines studied in this work. . . .

72

Table 2.4:

Selected He I emission properties for lines studied in this work.

. . .

72

Table 2.5:

PLTE criteria for He I and Ar II emissions. Argon Te is 1.5 eV and
the Ar II level under consideration is 4p 4Po 5/2. For Helium Te is
2.0 eV and He I level is 3p 1Po.
. . . . . . . . . . . . . . . . . . . .

76

Table 3.1:

Plasma properties used to study Maxwellization of the EEDF.

. . .

97

Table 3.2:

PLASIMO boundary conditions abbreviations.

. . . . . . . . . . . . 130

Table 3.3:

PLASIMO boundary conditions employed for PW models. . . . . . . 130

Table 3.4:

Characteristics of beam particle deflections from the PW for several
test beams each at 18 MeV/u. Beam particle is initially 1.5 mm from
center-axis and has zero angle.

. . . . . . . . . . . . . . . . . . . . . 139

Table 3.5:

Beam emittance values resulting from transit through the two PWs
enclosing a GCS (GCS not considered here). RMS emittance results
are for a 238U beam with charge state 33+ for PW1 and 73+ for
PW2, and each PW being 10 cm long and 150 A [1]. . . . . . . . . . 140

viii

LIST OF FIGURES

Figure 1.1: A figure published in Ref. [2], reproduced with permission. Cross
sections of electron capture and loss are shown, with the intersection
being the equilibrium charge state for the beam-stripper combination.

Figure 1.2: A figure published in Ref. [3], reproduced with permission. This il-
lustrates the damage caused by an 8.1 MeV/u 208Pb beam impinging
on a DLC foil. The left frame is an unused foil and the right frame
has accumulated a dose of 4-6x1014 ions of an approximately 2 mm
diameter beam spot.
. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.3: A figure published in Ref. [4], reproduced with permission. This
shows calculations of mean (stripped) charge state of original 238U35+
over a range of the beam’s initial energy.
. . . . . . . . . . . . . . .

Figure 1.4: Energy spread calculations performed by F. Marti (left figure pub-
lished in Ref. [3] and reproduced with permission, right figure unpub-
lished). This indicates the growth of energy spread in a 238U beam
initially of charge state 33+ passing through a 225 torr (left) and
375 torr (right) He gas charge stripper that is 30 cm long. Note the
change in ordinate scale.
. . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.5: A figure published in Ref. [3], reproduced with permission. This is a
calculation performed by P. Thieberger (Brookhaven National Lab).
A greater spread in the beam energy loss means there will be a greater
beam energy spread. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.6: Flow rates in argon (left) and helium (right) gases for a PW con-
sisting of six 6 mm aperture plates (6x6mm). Values in parentheses
correspond to value obtained as the flow through the channel at the
corresponding GCS pressure without the presence of the plasma arc.

Figure 1.7: Flow rates in argon (left) and helium (right) gases through a variety
of different PW channel configurations, all without presence of arc.
Quadratic fits to this data are used to extrapolate no-arc flows to the
GCS pressures studied in arc (100-400 torr).
. . . . . . . . . . . . .

Figure 1.8: Plasma electron density vs. electron temperature, created after simi-
lar figures in Refs. [5, 6]. The PW plasma characteristics would place
. . . .
it within the colored box ”High Pressure Arcs & Lightning”.

2

4

6

7

8

10

11

13

ix

Figure 1.9: A photo of the plasma window. Labeled components are as follows:
A. are the cathodes, B. are the cascaded plates (6 total in this image),
C. is the anode plate attached to an expansion chamber connected
to the vacuum pump assembly, and D. is the ion beam’s trajectory
through the plasma window, and the direction of gas flow. Outside
of this image on the left side is the GCS chamber.
. . . . . . . . . .

Figure 1.10: A Grotrian diagram illustrating the excitation level scheme of He I,
with the levels in orange being the metastable levels. Blue lines indi-
cate observed He I emissions that will be used to determine electron
temperature Te and electron density ne. The labels are the emission
. . . . . . . . . . . . . . . . . . . . . . . . . . .
wavelengths in nm.

Figure 2.1: A photo of the test stand, showing the section that includes the
plasma window and associated diagnostics, the gas charge stripper
chamber, and the main chamber. . . . . . . . . . . . . . . . . . . . .

Figure 2.2: Plasma window test stand schematic in fresh gas flow mode. Either
. . . . . . .

argon or helium is introduced via the gas cylinder feed.

16

24

29

29

Figure 2.3: Plasma window test stand schematic in recirculation gas flow mode.

Before operation, the buffer chamber is pressurized to around 12 PSI. 30

Figure 2.4: A photo of the region between GCS (shown on left side) and PW (out
of view on right side). A voltage supply maintains a -300 V relative
to the GCS in order to repel electrons that would generate an arc
upstream towards the GCS rather than downstream through the PW. 32

Figure 2.5: A photo showing another plasma window configuration, this time be-
ing a 8x6mm configuration and including several diagnostics used in
characterizing the plasma. A. is the gas inlet connected to GCS, B.
is one of the three cathodes inserted into the channel, C. are the PW
cascaded plates, D. are copper fingers connected to voltage measure-
ment setup described in Section 2.1.3.3, E. is the anode plate, and F.
are diagnostic plates.
. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.6: A photo of the components between PW plates and a bare plate. The
labels are as follows: A. is the FR4 insulator, B. is the FFKM o-ring,
C. is the alumina inner insulator, D. is the inner copper surface, E.
is the plasma channel, and F. are the water coolant entry and exit
ports. The top photo is of a cross sectional view of the plate, showing
the coolant channel position and size.
. . . . . . . . . . . . . . . . .

33

34

x

Figure 2.7: A photo showing the components of the plasma window’s cathode
structures. A is the W-ThO2 cathode tip, B an alumina jacket, C a
Vespel insulator, D a FFKM o-ring, E a nut to affix the structure to
the housing, F the water-cooled copper holder, G the water inlet and
outlet, and H the cathode housing. . . . . . . . . . . . . . . . . . . .

Figure 2.8: A photo indicating the dimensions of the exposed 2% by mass W-
ThO2 cathode tip inside the copper shield. This is a zoomed view of
. . . . . . . . . . . . . . . . . . . . . . .
component A in Fig. 2.7.

Figure 2.9: A drawing of the PW and part of the Main Chamber. The cone is
also shown which acts as a heat sink for the hot plasma in the main
chamber.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.10: A photo looking through the viewport of the main chamber. The
cone is visible, being bathed in the argon plasma exiting the PW. . .

Figure 2.11: A diagram showing the plasma window circuit. Pairs of PW power
supplies are in series with inductors and water cooled resistors to
provide stability to voltage fluctuations. Three of these sets are in
parallel, leading to the PW load. . . . . . . . . . . . . . . . . . . . .

Figure 2.12: A photo of the gas-feed components of the PW. The GCS chamber
can be partly seen in the top left corner of the photo, and the PW is
even farther left (out of view here).
. . . . . . . . . . . . . . . . . .

Figure 2.13: A photo indicating the setup of the diagnostic plate. The copper
diagnostic plate itself can be seen positioned at P2/6 here. The di-
agnostic plate’s fiber optic feedthrough and pressure sensor are also
visible on the outward side of the diagnostic arm which is grounded.
An insulating break separates this grounded side from the floating
voltage of the plate.
. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.14: Cross sectional diagram of the plasma window and the primary com-
ponents which comprise it . The insulating components and o-rings
between the plates are shown in Fig. 2.6, and the cathode compo-
. . . . . . . . . . . . . . . . .
nents are shown in Figs. 2.7 and 2.8.

Figure 2.15: Sample acquisitions of both ambient null (left) and chiller cycle null
. . . . . . . . . . . . . . . . . . . . . . . . . .

temperature values.

Figure 2.16: Sample spectra obtained from a 6x6mm PW, the vantage point be-
ing across a diagnostic plate positioned at P6/6. The spectra were
collected with integration times of 800 ms and 50 ms for helium and
argon respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

37

38

39

40

40

42

43

47

49

xi

Figure 2.17: Differential rate constant for electron-impact ionization from the lowest-

lying metastable level as well as directly from ground level, for both
argon and helium. The argon test case has Te = 1.5 eV and the
helium has Te = 2.1 eV. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.18: Similar to Fig. 2.17 but for excitation, this is the differential rate
constant for electron-impacts to the lowest-lying metastable level as
well as directly from ground level, for both argon and helium. The
argon test case has Te = 1.5 eV and the helium has Te = 2.1 eV. The
upper level is 5p [3/2]1 for argon and 4d 3D for helium.
. . . . . . .

Figure 2.19: Reproduction of figure published in Ref. [7]. This qualitatively il-
lustrates the perturbations of two energy states originally of energy
E1 and E2 as a function of charged perturber distance R from the
emitter. The perturbed energies V1 and V2 set the emitted photon
energy hν. Perturber particle is denoted as P e and emitter particle
as Em.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.20: Reproduction of figure published in Ref. [8], illustrating changes to
the microfield distribution with deviations from the Holtsmark distri-
bution (R = 0), 
 is in units of 
0. Symbols are different than those
used in the thesis: the Debye shielding parameter symbol is a, the
field strength is 
, the normal Holtsmark field strength is 
0, and the
normalized distribution function is P (
). . . . . . . . . . . . . . . . .

Figure 2.21:

Instrumental profiles for the Ocean Optics HR4000 spectrometer used
in this project. These profiles were acquired using a low pressure He
gas discharge lamp.
. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.22: Sample Stark fits for the Ar I 425.9 nm and He I 447.1 nm emis-
sions respectively, for a representative operating condition of 200 torr
(150 torr for He) and 150 A in a 6x6mm PW, collected at P6/6. In-
strumental profiles obtained by low pressure lamp discharge are also
shown. A forbidden component on the blue wing of the primary He
peak is also seen (this is not fitted).
. . . . . . . . . . . . . . . . . .

Figure 2.23: View of the NSCL PW cathode tips from inside the cathode housing,
looking down the channel towards the anode. Banding structure is
visible on the used ThO2-W cathodes, signifying regions of varying
. . . . . . . . .
thorium concentrations, as described in Refs. [9–11].

Figure 2.24: Cathode housing (without cathodes), view from the PW-side face.
The housing channel is 13 mm diameter, which then constricts down
to 6 or 10 mm diameter, depending on the aperture of the first PW
plate.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

52

58

60

65

67

81

82

xii

Figure 2.25: Top-Left: Thoriated tungsten cathodes after about 30 minutes of op-
eration. Bottom-Left: Pure tungsten cathodes after about 30 minutes
of operation. Right: Zoom of the pure tungsten cathodes, illustrating
neck reduction and formation of surface roughness. . . . . . . . . . .

Figure 2.26: From data published in Ref. [12], this figure shows vapor pressures of
. . .

metallic thorium and lanthanum as a function of temperature.

Figure 2.27: Left: A photo of PW cathodes after operation in He gas, showing
a series of bands at different distances from the cathode tip. Right:
a copy of a figure published in Ref. [10] which investigated similar
behavior for thoriated tungsten cathodes operating in helium. Their
surface morphology studies enabled identification of the bands as la-
beled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.1: Maxwellian EEDFs for two electron temperatures, one typical of Ar
PW discharges (black solid line) and one typical of He PW discharges
(red dot-dashed line). For that element’s corresponding line, drop
lines are given for the lowest-lying excited state and ionization ener-
gies, as well as at 4.5 eV (close to the value for ionization from the
lowest metastable level for both gases).
. . . . . . . . . . . . . . . .

Figure 3.2: The ratio of inelastic process rates from ground state, to the electron-
electron collision rate neνee. The inelastic process rate is determined
as a function of energy, so that an occurrence is triggered only from
electrons at energy E. On the other hand, the electron-electron col-
lision rate is the rate over the entire EEDF. . . . . . . . . . . . . . .

84

89

90

95

98

Figure 3.3: Results of BOLSIG+ calculations by applying the operating condi-
tions for He OC2 and Ar OC2 in Tab. 3.1. Shown also are the
effective electron temperatures. Dotted lines are the EEDFs solved
for by BOLSIG+ and solid lines are the corresponding Maxwellian
EEDFs whose electron temperature Te matches the effective temper-
ature Tef f of the dotted line EEDF.

. . . . . . . . . . . . . . . . . 100

Figure 3.4: Matching Parameter for HeCRM synthetic spectra compared to mea-
sured spectra of a 200 torr GCS pressure, 120 A arc in 6x6mm PW
geometry, at two measurement locations. The model was initialized
for P2/6 with ne = 2.0 × 1015 cm-3 and ng = 1.1 × 1017 cm-3, and
for P6/6 with ne = 1.5 × 1015cm-3 and ng = 6.6 × 1017cm-3 (ne from
measurement and ng from PLASIMO model).

. . . . . . . . . . . . 105

xiii

Figure 3.5: Measured and synthesized irradiances corresponding to the selected
both the lower and upper matching temperature values in Fig. 3.4
(Tlo and Thi). The temperature Thi is selected as the electron tem-
perature.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 3.6: Argon plasma viscosity calculated using Chapman-Enskog kinetic
theory described above. Viscosity values are calculated at three dif-
ferent ionization degrees to illustrate their impact. The black curve is
that obtained by Murphy and Arundell [13] in which the assumption
of Saha ionization equilibrium is taken.

. . . . . . . . . . . . . . . . 121

Figure 3.7: Mesh used for the PLASIMO 6x6mm PW model, in which the “x
[m]” axis corresponds to the axial, or z-direction and the “y [m]”
axis corresponds to the radial, or r-direction. The cathode and gas
entry side is the west edge and the anode and gas exit side is the east
edge, the north edge is the plasma-facing side of the enclosing metal
plates, and he south edge is the axis of symmetry. In the vicinity of
the west, east, and north edges, the mesh spacing is condensed for
greater numerical stability.

. . . . . . . . . . . . . . . . . . . . . . . 128

Figure 3.8: Measured plate pressures in argon and helium arcs of a 6x6mm PW,
expressed as fraction of the GCS pressure. Plate pressures are given
at the measured plate locations of P2/6 (left) and P6/6 (right, note
the change in ordinate scales). Linear extrapolation of these pressures
to the PLASIMO model region inlet and outlet provides the BCs used
at those locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Figure 3.9:

Several plasma properties from a PLASIMO model of a 6x6mm PW
of argon at GCS pressure 200 torr and arc current 120 A.

. . . . . . 133

Figure 3.10: Similar to Fig. 3.9 but for helium. Several plasma properties from
a PLASIMO model of a 6x6mm PW of helium at GCS pressure 200
torr and arc current 150 A. . . . . . . . . . . . . . . . . . . . . . . . 134

Figure 3.11: PLASIMO arc current for a 1x6mm 5x10mm model corresponding to
a PW with 200 torr GCS pressure and 120 A arc current. There is
a mismatch not only between the arc current in the two sections but
also between both and the experimental arc current. . . . . . . . . . 135

Figure 3.12: A diagram illustrating the orientation of an ion beam traversing the
PW-GCS arrangement. Also shown are the magnetic field orienta-
tions from the PWs and the resulting deflection on a beam particle.

137

xiv

Figure 3.13: Two possible scenarios for beam Courant-Snyder ellipses at the en-
trance of the GCS. Beam-gas scatterings will cause angular deflec-
tions, growing the ellipse in the x(cid:48), y(cid:48) directions, and will have a
greater overall area growth for Case 2. . . . . . . . . . . . . . . . . . 141

Figure 4.1: Argon flow (left) and flow reduction factor (right) data taken in mul-
tiple PW configurations, labeled A-G. All data is for a GCS pressure
of 200 torr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Figure 4.2:

Similar to Fig. 4.1 but for helium. Helium flow and flow reduction
factor data taken in multiple PW configurations, labeled A-G as in
Fig. 4.1, however due to experimental limitations no data was ac-
quired for configurations D or G, and data for F was extrapolated
from data at other pressures in that configuration. All data is again
for a GCS pressure of 200 torr. . . . . . . . . . . . . . . . . . . . . . 144

Figure 4.3:

Simulated relative radial intensities for three selected emissions for a
6x6mm PW, using PLASIMO modeled data corresponding to P2/6,
GCS pressure 200 torr, and arc current 150 A. The dashed line is an
exponential decay fit, representing the radial intensity distribution
e(r) to be used.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Figure 4.4: Normalization factors for reconstructing a would-be-observed Stark
profile from PLASIMO measurements. The black solid line is the
geometric normalization using Eqs (4.1) and (4.2), the red dotted
line is the emission normalization factor from Fig. 4.3, and the blue
dash-dotted line is the (renormalized) product of the other two curves.
The green dash-dot-dot line is the cumulative integration of the blue
overall factor.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Figure 4.5:

Stark profiles at selected radii, using overall normalization factors
from Fig. 4.4. The profiles are constructed using Stark parameters
corresponding to radial electron densities determined by PLASIMO
for an argon 6x6mm PW, GCS at 200 torr and 120 A, at the axial
location corresponding to P6/6.

. . . . . . . . . . . . . . . . . . . . 151

Figure 4.6: Reconstructed Stark profiles without any reabsorption as well as with,
at two different absorber densities. This is for a 6x6mm PW, GCS at
200 torr and 120 A for both gases, at the axial location corresponding
to P6/6.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

xv

Figure 4.7:

Figure 4.8:

Left: The overall reconstructed profile and corresponding Stark fit
using PLASIMO radial electron densities for an argon 6x6mm PW,
GCS at 200 torr and 120 A, at the axial location corresponding to
P6/6. Right: Comparison of various Stark widths. Black points
are PLASIMO modeled values at radial values inside arc channel.
The green solid line represents the Stark width measured during PW
operation, and the orange dot-dashed line represents the Stark width
of the fit to the PLASIMO overall reconstructed profile.

. . . . . . . 154

Left: The overall reconstructed profile and corresponding Stark fit
using PLASIMO radial electron densities for a helium 6x6mm PW,
GCS at 200 torr and 120 A, at the axial location corresponding to
P6/6. Right: Comparison of various Stark widths. Black points
are PLASIMO modeled values at radial values inside arc channel.
The green solid line represents the Stark width measured during PW
operation, and the orange dot-dashed line represents the Stark width
of the fit to the PLASIMO overall reconstructed profile.

. . . . . . . 155

Figure 4.9: Electron densities in argon arc at two axial locations along the 6x6mm
PW channel. The data set at left is taken at plate 2/6 and the
data set at right is at plate 6/6. Comparisons with corresponding
PLASIMO model electron densities at those axial locations are shown
also obtained by a Stark fit to an overall reconstructed Stark profile. 156

Figure 4.10: Similar to Fig. 4.9 but for helium. Electron densities in helium arc
at two axial locations along the 6x6mm PW channel. The data set
at left is taken at plate 2/6 and the data set at right is at plate 6/6.
PLASIMO comparison data also shown. . . . . . . . . . . . . . . . . 157

Figure 4.11: Electron density in argon PW for two different configurations, a
6x6mm (left) and 6x10mm (right). In both cases the electron densi-
ties are for P6/6.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Figure 4.12: Electron temperature at plate 2/6 and plate 6/6 as determined by
Boltzmann line method with Ar II lines in a 6x6mm argon PW. Dot-
ted lines and open points show the result from PLASIMO model
corresponding operating conditions. The model values have been in-
tegrated over the channel radius at the relevant axial location.

. . . 161

Figure 4.13: Measured excitation temperature Texc from Boltzmann line method
(left), and electron temperature Te from comparison of measured rel-
ative intensities to those calculated using HeCRM. The top two plots
pertain to plate 2/6 and the bottom two pertain to plate 6/6. Note
the difference in scales of the y-axes. . . . . . . . . . . . . . . . . . . 162

xvi

Figure 4.14: Electron temperature at plate 2/6 and plate 6/6 as determined by
Boltzmann line method with He I lines in a 6x6mm helium PW.
The collisional-radiative model [14, 15] in conjunction with measured
electron densities from Fig. 4.10 to determine these electron temper-
atures. Dotted lines and open points show the result from PLASIMO
model corresponding operating conditions. The model values have
been integrated over the channel radius at the relevant axial location. 163

Figure 4.15: Electric field in argon 6x6mm PW with GCS pressure 200 torr, calcu-
lated from floating plate voltages. The inset is the derivative of this
electric field with respect to axial position.

. . . . . . . . . . . . . . 164

Figure 4.16: Similar to Fig. 4.15 but for helium. Electric field in helium 6x6mm
PW with GCS pressure 200 torr, calculated from floating plate volt-
ages. The inset is the derivative of this electric field with respect to
axial position.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Figure 4.17:

Inner electric field strengths Ein for arcs in 6x6mm PW at various
GCS pressures and arc currents. The region’s starting point is defined
as between plates 2 and 3, and the ending point is defined as between
penultimate and final pre-anode plate. . . . . . . . . . . . . . . . . . 166

Figure 4.18: Electrical conductivity of the arc for several currents in a 6x6mm
argon PW with GCS pressure at 200 torr. PLASIMO model results
are shown as well. The model values have been integrated over the
channel radius at the relevant axial location.

. . . . . . . . . . . . . 167

Figure 4.19: Similar to Fig. 4.18 but for helium. Electrical conductivity of the
arc for several currents in a 6x6mm helium PW with GCS pressure
at 200 torr. PLASIMO model results are shown as well. The model
values have been integrated over the channel radius at the relevant
axial location.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Figure 4.20: Power removed by water coolant for each PW plate in a 6x6mm
configuration in argon arc. Each data set is taken at a GCS pressure
of 200 torr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Figure 4.21: Similar to Fig. 4.20 but for helium. Power removed by water coolant
for each PW plate in a 6x6mm configuration in helium arc. Each
data set is taken at a GCS pressure of 200 torr. . . . . . . . . . . . . 171

xvii

Figure 4.22: Shown are data from two separate collections from a 6x6mm PW
in helium gas, one which had a single diagnostic plate at plate 2,
and one which had a single diagnostic plate at plate 6. For both,
GCS pressure was 200 torr and arc current was 120 A. At left is the
power deposited to the plates determined by calorimetry and at right
are voltage drops between adjacent plates. Circled regions highlight
where behavioral differences between the two collections would be
expected due to the diagnostic plate’s presence or lack thereof.

. . . 172

Figure 4.23: PLASIMO viscosity values for argon 6x6mm PW at axial points along
arc channel. The viscosities were obtained by averaging over the inner
3/4 of the full channel radius. Left: GCS pressure at 200 torr and
various currents. Right: GCS pressure at 150 A and various GCS
pressures. The room temperature gas viscosity of argon is about
2.2 × 10−5 Pa*s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Figure 4.24: Similar to Fig. 4.23 but for helium. The room temperature gas

viscosity of helium is about 2.0 × 10−5 Pa*s.

. . . . . . . . . . . . . 175

Figure 4.25: PLASIMO ionization degree values for argon 6x6mm PW at axial
points along arc channel. These were obtained by averaging over the
inner 3/4 of the full channel radius. Left: GCS pressure at 200 torr
and various currents. Right: GCS pressure at 150 A and various GCS
pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Figure 4.26: Similar to Fig. 4.25 but for helium.

. . . . . . . . . . . . . . . . . . 177

(cid:115)

n2
n(cid:48)
h

h

(cid:113)−P(cid:48)

Figure 4.27: The density factor

in argon plasma, determined via PLASIMO

models of various operating conditions in a 6x6mm PW. . . . . . . . 178

Figure 4.28: Similar to Fig. 4.27 but for helium.

. . . . . . . . . . . . . . . . . . 178

Figure 4.29: The pressure drop factor

p in argon plasma, determined via

PLASIMO model of various operating conditions in a 6x6mm PW. . 179

Figure 4.30: Similar to Fig. 4.29 but for helium.

. . . . . . . . . . . . . . . . . . 179

Figure 4.31: Ratio of electron collisional heating and viscous heating of the heavy

particles for a variety of PLASIMO modeled conditions.

. . . . . . . 180

Figure 4.32: Similar to Fig. 4.32 but for helium.

. . . . . . . . . . . . . . . . . . 180

xviii

Figure 4.33: Flow rates in the 6x6mm PW configuration for both argon (left) and
helium (right). Both measurements (solid points) and corresponding
PLASIMO model values (open points) are shown. The different colors
represent different GCS pressure settings.

. . . . . . . . . . . . . . . 181

Figure 4.34: Flow rate in a 6x6mm PW and 8x6mm PW at various GCS pressures

and arc currents in both argon and helium.

. . . . . . . . . . . . . . 182

Figure 4.35: Flow rate reduction (FRF) in a 6x6mm PW and 8x6mm PW at var-

ious GCS pressures and arc currents in both argon and helium. . . . 183

Figure 4.36: Flow rate reduction (FRF) in a 6x6mm PW and 8x6mm PW at var-
ious GCS pressures, plotted against retained arc power (rather than
current as in Fig 4.35).

. . . . . . . . . . . . . . . . . . . . . . . . . 184

Figure 4.37: Measured electron temperature (right) and density (left) values in
both a 1x6mm 5x10mm and 1x6mm 9x10mm PW in argon with GCS
pressure of 200 torr. Also shown are corresponding PLASIMO model
values. All properties are determined at the P1/6 or P1/10 position. 186

Figure 4.38: Measured electron density at plate 1 in 1x6mm 5x10mm (left) and
1x6mm 9x10mm PW (right) PW configurations in argon for a variety
of GCS pressures and arc currents.

. . . . . . . . . . . . . . . . . . 187

Figure 4.39: Measured electron temperature at plate 1 in 1x6mm 5x10mm (left)
and 1x6mm 9x10mm PW (right) PW configurations in argon for a
variety of GCS pressures and arc currents.

. . . . . . . . . . . . . . 188

Figure 4.40: Voltage drops between PW components in a 1x6mm 7x10mm PW for
both argon (left) and helium (right) arcs. For all cases, GCS pressure
is 200 torr. Some of the PW components between which a data point
is taken are labeled on the left plot. Those without labels are taken
as between two adjacent plates, similar to the labeled P1-P2 point,
and though not indicated, the left plot points follow identical labelings.189

Figure 4.41: Photos of cathodes and their holders after attempting an arc in helium
PW of 6x10mm configuration, which ultimately proved too unstable
for data collection. The copper shield has been deformed and just
below on the left photo there is an indentation in the copper holder,
possibly due to this acting as an emission site.

. . . . . . . . . . . . 192

Figure 4.42: A pictorial representation of the undesired copper bridging effect that
often occurs for cathode-side plates. Also shown are different possible
insulator designs that may inhibit the copper bridging effect.

. . . . 194

xix

Figure 4.43: Left: A photo of dramatic and rapid copper removal from P1 in a
1x6mm 9x10mm PW operated in helium at 300 torr GCS pressure,
210 A arc current. Middle: The remove material was redeposited
along the channel wall downstream of the removal site. Right: The re-
sult of continued copper surface removal, which has here cut through
to the water coolant path, resulting in even more extensive damage.

195

Figure 4.44: The three thoriated tungsten cathodes after a 6-day continuous oper-
ation run in helium at GCS pressure 300 torr and 180 A arc current.
Also shown for comparison is an unused cathode. . . . . . . . . . . . 197

Figure 4.45: Spectral acquisitions at several different times, of two narrow wave-
length windows. The Ar II emissions can clearly be seen to persist
for several minutes after switching from argon to helium gas. This
data was taken in fresh gas (expelled to atmosphere), not recirculation.199

Figure 4.46: Arc power for various arc currents GCS pressures in the PW config-

uration of 6x6mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Figure 4.47: Arc power for various arc currents GCS pressures in the PW config-

uration of 8x6mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Figure 4.48: Arc power for various arc currents GCS pressures in the PW config-

uration of 1x6mm˙7x10mm. . . . . . . . . . . . . . . . . . . . . . . . 202

Figure 4.49: Arc power for various arc currents GCS pressures in the PW config-

uration of 1x6mm˙9x10mm. . . . . . . . . . . . . . . . . . . . . . . . 203

Figure 4.50: Arc power for various arc currents GCS pressures for two the PW
configurations, both of which are for argon arc. The left plot is for
6x10mm configuration and the right plot is for 1x6mm˙5x10mm.

. . 203

Figure 4.51: An empirical scaling relationship between operating conditions and
flow rate. Each PW configuration shown includes the multitude of
operating conditions explored within that configuration. . . . . . . . 206

xx

KEY TO ABBREVIATIONS

BC

Boundary Condition

CCRF Capacitively Coupled Radio Frequency

CR

DC

Collisional Radiative

Direct Current

DLC

Diamond-Like Carbon

DRC

Differential Rate Constant

EEDF Electron Energy Distribution Function

FRIB

Facility for Rare Isotope Beams

GCS

Gas Charge Stripper

LOS

Line of Sight

LTE

Local Thermodynamic Equilibrium

MP

Matching Parameter

MSU Michigan State University

NSCL National Superconducting Cyclotron Laboratory

OES

Optical Emission Spectroscopy

PLTE Partial Local Thermodynamic Equilibrium

PW

WF

Plasma Window

Work Function

xxi

Chapter 1

Introduction

1.1 Charge Stripping

Charge stripping is an increasingly necessary process in a high energy ion accelerator. Gen-

erally in accelerator facilities, heavy ions emerge from the ion source with a relatively low

charge state distribution. Further stripping of electrons reduces total RF voltage required to

accelerate to a given energy or enables higher attainable energies for a facility with a given

total RF voltage [3, 16]. To understand the mechanism of charge stripping, consider that as

the ion beam impinges upon the charge stripping media, the ions can capture or relinquish

electrons to the target atoms. Cross sections for these processes depend upon the ion’s prop-

erties: species, charge state, and energy. For a given beam energy, there exists some beam

charge state such that the cross section for electron capture and electron loss are equivalent

(or as close to equivalent as any integer charge state can allow). This charge state is therefore

called the equilibrium charge state for that particular beam/stripper combination at that

energy, with a charge state distribution forming about this equilibrium state [2, 16, 17]. An

example of this is shown in Fig. 1.1, a reproduction of a figure published in Ref. [2], which

illustrates electron loss and capture intersections as a function of charge state for several

beam energies. The beam here is uranium with the stripper being helium gas. It should be

noted that the charge stripper requires a material thickness sufficiently great for the beam

1

Figure 1.1: A figure published in Ref. [2], reproduced with permission. Cross sections of
electron capture and loss are shown, with the intersection being the equilibrium charge state
for the beam-stripper combination.

to attain this equilibrium charges state before exiting the charge stripper.

In the National Superconducting Cyclotron Laboratory (NSCL) where the research of

this thesis was conducted, the primary application of the accelerator is for nuclear physicists

and chemists to study the nature of nuclei, usually those that are short-lived, or “rare”.

The accelerator facility is usually operated to produce a given ion beam of stable nuclei

which then impinges on a low-Z target to produce the radioactive nuclei whose properties

in terms of nuclear structure or subsequent reactions are investigated, in processes that

are often rare and statistics-limited. Statistical limitations in these rare processes will be

greatly relaxed in the successor Facility for Rare Isotope Beams (FRIB), which will nominally

provide more than 2 orders of magnitude greater beam intensity, largely by increased particle

count [18, 19]. This substantially higher ion beam intensity necessitates a charge stripper

which can operate continuously on the timescale of the typical nuclear science experiment

2

- up to 2 weeks. Traditionally, solid charge strippers have been used, primarily diamond-

like-carbon foils. However as accelerator facilities continue to push the intensity frontier, the

lifetime of the foils diminishes substantially, and even for facilities currently in development

such as the Facility for Rare Isotope Beams (FRIB), the kinetic impact damage sustained by

these foils from the beam, also called radiation damage in the charge stripping community,

would render them unusable in a matter of minutes to seconds. The foils suffer thinning

from the energetic ion impingements, an effect called the “ion hammering effect” reducing

the stripping efficiency. The foils furthermore suffer rapid and localized heating at the beam

spot, resulting in sublimation which is the primary lifetime-limiting factor for beam current

densities in excess of about 20 pA/cm2 [3]. Much more detail describing the processes

taking place particularly in beam-solid stripper material can be found in Refs. [3, 16]. For

the purposes of nuclear physics and chemistry experiments that take place in the National

Superconducting Cyclotron Laboratory (NSCL) and the upcoming successor facility FRIB,

the beam is required to be utilized often for 1-2 weeks continuously. The charge stripper

should be usable and stable over this entire duration.

As a result, the use of charge strippers that can be readily regenerated after beam in-

teraction, such as gas or liquid, is rapidly becoming a necessity; indeed, for FRIB, it is

already a necessity. More details on the topic of liquid charge strippers can be found in

Refs. [20, 21] which discuss a liquid lithium charge stripper (the baseline for FRIB), and the

review in Ref. [3] also details other liquid stripper possibilities. Gas charge strippers (GCS)

face their own set of challenges which need to be addressed for them to be viable choices

in high intensity heavy ion accelerators. Namely, gas charge strippers: yield lower charge

state distributions than solid counterparts; can introduce substantial energy spread to the

beam; necessarily require a more sophisticated system for containment; and can result in

3

Figure 1.2: A figure published in Ref. [3], reproduced with permission. This illustrates the
damage caused by an 8.1 MeV/u 208Pb beam impinging on a DLC foil. The left frame is an
unused foil and the right frame has accumulated a dose of 4-6x1014 ions of an approximately
2 mm diameter beam spot.

beam emittance growth attributed to the GCS having a long interaction region compared to

a solid charge stripper. The charge stripping gas must be in a continuous flow, around 100

m/s, as a sort of curtain to remove stripper material that is heated by the gas so it can be

cooled and recirculated.

A property of charge strippers with which they can be characterized is using the target

thickness, defined as the target density multiplied by the interaction length, generally given

in µg/cm2 as:

µ = ρL =

mP
kT

L .

(1.1)

Here, ρ is the stripper density, m the gas mass, P the GCS pressure, k Boltzmann’s constant,

T the GCS temperature, and L the GCS length. For gases, this means that a given target

thickness can be maintained by exchanging a shortening of GCS length L for an increase

4

in GCS pressure P . The target thickness µ is what impacts the transiting beam’s energy

spread, but greater length will result in an undesired effect of increased beam size, due to

angular dispersion induced from beam-stripper scatterings and space charge effects, and as

a result, the beam’s emittance will continually grow throughout. For this reason, achieving

the desired target thickness µ is ideally achieved by having a large GCS pressure P and a

short GCS length L. For an ion beam of a certain initial energy impinging on a gas charge

stripper target, there is an optimum thickness for maximizing the outgoing mean charge state.

Ideally this mean charge state would be the equilibrium charge state. This optimization

exists because of a balance between competing effects:

increasing thickness enables more

interactions with the stripper, allowing the beam to achieve the equilibrium charge state

distribution. However, further increases to the target thickness result in increased energy

attenuation which decreases the equilibrium charge state distribution. This effect can be

seen in Fig. 1.3. Selecting a single initial energy of 238U beam to examine and comparing

the mean charge state at different target thicknesses, it is clear the competing effects of

increased charge-stripping interactions and greater energy attenuation result in an optimum

GCS thickness for that particular initial beam energy. Target thicknesses both greater and

lesser than this optimum value yield a lower mean charge. Additionally, this optimum

thickness shifts to ever greater values as incident beam energy increases. For example the

optimum thickness is about 2 mg/cm2 at an energy of 14 MeV/u but about 4 mg/cm2 at

an energy of at 18 MeV/u.

Currently, the Radioactive Isotope Beam Factory, a facility of Japan’s RIKEN uses a

helium GCS maintained around 50 torr [2, 4, 22, 23] and the FAIR facility at Germany’s GSI

has a pulsed GCS which provides peak pressure of around tens of torr which is sufficient for

the low duty factor accelerator’s needs [24–26]. For RIKEN, the beam energy at the charge

5

Figure 1.3: A figure published in Ref. [4], reproduced with permission. This shows calcula-
tions of mean (stripped) charge state of original 238U35+ over a range of the beam’s initial
energy.

stripper is about 11 MeV/u, so based on Fig 1.3, the required target thickness for a 11

MeV/u U beam to achieve the equilibrium charge state is substantially lower than thickness

required for achieving the equilibrium charge state for a 18 MeV/u U beam at FRIB.

The beam’s interaction with the GCS also imposes a large power deposition, on the order

of 1% of the beam power. Consider a beam that is 18 MeV/u 238U, with current 350 eµA

(hypothesized typical FRIB beam current for species O-U [27]) and transverse beam size of

1 mm diameter. For this beam impinging on a 300 torr, initially room temperature helium

gas over a distance of 0.3 m, this corresponds to a power deposition of about 430 W and 1800

W/cm3. An approximate calculation of the temperature rise of the helium gas in this beam-

interacting column can be made by taking the specific heat of helium at standard temperature

and pressure of 5.193 J/g*K, and supposing that the helium is flowing perpendicular to the

beam trajectory at a rate of 100 m/s. With these conditions, the temperature increase of

6

Figure 1.4: Energy spread calculations performed by F. Marti (left figure published in
Ref. [3] and reproduced with permission, right figure unpublished). This indicates the growth
of energy spread in a 238U beam initially of charge state 33+ passing through a 225 torr
(left) and 375 torr (right) He gas charge stripper that is 30 cm long. Note the change in
ordinate scale.

the column of helium initially occupying the same volume as the beam is about 54 K.

Related to this is the issue of energy spread resulting from the ion beam’s passage through

the gas charge stripper. Simulations have been conducted by F. Marti [3] and P. Thieberger

therein to assess the degree of energy spread the GCS introduces to the beam. In Fig. 1.4 an

example of the energy spread evolution in 225 torr and 375 torr He gas charge strippers that

are 30 cm long. The energy spread results from the beam heating the gas, which causes its

density and therefore target thickness to change. In Fig. 1.5, another simulation published

in Ref. [3] is shown, this one performed by P. Thieberger which illustrates the relative degree

of energy spread in the outgoing beam after having transited a gas stripper with a single

curtain of flowing stripper gas (as described above), as well as a gas stripper with two flowing

curtains of opposing direction (red solid curve). This suggests that the differences in stripper

heating can be mitigated by having multiple, direction-alternating curtain flows of stripper

gas.

7

Figure 1.5: A figure published in Ref. [3], reproduced with permission. This is a calculation
performed by P. Thieberger (Brookhaven National Lab). A greater spread in the beam
energy loss means there will be a greater beam energy spread.

As mentioned above, the other challenge of gas charge strippers is that they require a

system dedicated to containing the high pressure gas to prevent gas leakage to the upstream

and downstream beamline. The GCS must be open-ended, since the ion beam would simply

damage and ultimately bore through any solid walls containing the gas. This fact means that

the contents of the GCS will leak out of the containing chamber at a rate related to the aper-

ture size, since the conductance scales as the aperture area. To maintain constant pressure,

the chamber must be constantly filled at the same rate that it leaks; this is accomplished

differential pumping and recirculating the totality of the escaping gas. At beam energies

between 10-20 MeV/u, helium gas yields the highest charge state distributions [2, 22]. How-

ever its diffuses easily due to its low mass. This results in great difficulty in maintaining a

chamber of sufficient pressure for charge stripping while simultaneously preventing the gas

8

from flooding the rest of the beamline [23]. Maintaining low beamline pressure is a necessity

to avoid unexpected interactions with background gas which would cause beam scattering

and charge-exchange events, both of which would contribute to beam loss.

It is for this reason that a plasma window (PW) merits consideration, as it can greatly

limit the gas leakage rate from a GCS operating at required pressures. This gas flow rate

restriction is apparent when comparing the gas leakage rate through the PW channel from

a given GCS pressure without arc to that when the arc is active, as illustrated in Fig. 1.6.

A significant reduction in the rate of flow is observed, particularly for smaller diameter

aperture channels, a fact that will be shown and explored in Chapter 4. The flow rate is

restricted more with increasing current supplied to the arc. The conventional rationale for

this behavior is that increasing temperature in the arc results in an increase in viscosity

which inhibits the flow. It will be shown in Section 4.2.6 that this viscosity hypothesis isn’t

fully realizable under quantitative scrutiny, although the increasing temperature still plays

a significant role.

In Fig. 1.6, the values included in parentheses next to the curves represent the flow rates

corresponding to the respective GCS pressure without the presence of arc, merely a gas flow.

It must be pointed out that these GCS pressures are actually not attainable with this PW

test stand; the overall conductance is limited by the gas feed lines upstream of the PW

and GCS, and is too small to allow most of these pressures to be achieved. Therefore, the

values in parentheses are obtained by fitting to flow rates obtained at lower pressures and

extrapolating to the higher ones. Measured flow rates through the PW channel without the

presence of the arc are shown in Fig. 1.7. These flow rates are shown for several different

PW channel configurations (or plate geometries), which are described in more detail along

with an explanation of notation in Section 2.1.2. Note that by examining Figs. 1.6 and 1.7

9

Figure 1.6: Flow rates in argon (left) and helium (right) gases for a PW consisting of six
6 mm aperture plates (6x6mm). Values in parentheses correspond to value obtained as the
flow through the channel at the corresponding GCS pressure without the presence of the
plasma arc.

10

60901201501802100123456789101160901201501802100510152025303540455055Flow Rate [SLM]Current [A] 150 torr 200 torr 250 torr 300 torr 350 torr 400 torr(No-Arc: 51 SLM)(71 SLM)(93 SLM)(118 SLM)(145 SLM)ArgonHelium(430 SLM)(339 SLM)(255 SLM)(No-Arc: 178 SLM)Current [A]Figure 1.7: Flow rates in argon (left) and helium (right) gases through a variety of different
PW channel configurations, all without presence of arc. Quadratic fits to this data are used
to extrapolate no-arc flows to the GCS pressures studied in arc (100-400 torr).

that flow reduction rates for this geometry and these operating conditions are 10-24 for argon

and 7-14 for helium. This significant flow reduction broadens the range of applicability of

GCS applications.

1.2 Plasma

Plasmas span a vast array of conditions and regimes, as seen in Fig 1.8, but have some

characteristics in common. Plasmas display behavior referred to as collective effects. This

11

0204060801001200246810121416182022242628300204060801001200102030405060708090100110120130ArgonFlow Rate [SLM]GCS Pressure [torr] 6x6mm Plates 8x6mm Plates 1x6mm_5x10mm Plates 1x6mm_7x10mm Plates 1x6mm_9x10mm Plates 6x10mm PlatesHeliumGCS Pressure [torr]means that behavior of the entire plasma depends on the coupled behaviors of the individual

constituents of the plasma (electrons, ions, and neutrals). An arc plasma is a class of plasma

discharge that corresponds to currents in excess of about 1 amp and voltage drops of hundreds

of volts across the arc [28].

Due to the high mobility of electrons in a plasma, the media is highly conductive and

easily transmits current. Generally in plasmas, charge quasineutrality is assumed [5].

In

this condition, the plasma is considered to be overall charge neutral and the plasma electron

density ne about equal to the ion density ni in the bulk of the plasma, if only singly-ionized

charge states of the gas species are present. The condition does not hold in certain locations

such as near the cathodes, anode, and the enclosing walls. Here, “near” generally means

several times a characteristic length called a Debye length. This is the length scale over

which the electric field of any given plasma electron or ion is screened by oppositely charged
neighbors by a factor 1/e (e (cid:39) 2.72) of what it would be without the presence of screening

particles and is defined as [6]:

(cid:115)

λD =


0kTe
e2ne

,

(1.2)

in which 
0 is the perimittivity of free space, k the Boltzmann constant, Te is the electron

temperature, e the elementary charge, and ne the electron density (which is also equal to

ion density ni in quasineutral regions as mentioned above).

1.2.1 Cascaded Arc Discharge

As mentioned above, An arc plasma is a class of plasma discharge that corresponds to

currents on the order at least 1 A, across a voltage drop typically on the order of 100 V [28].

12

Figure 1.8: Plasma electron density vs. electron temperature, created after similar figures
in Refs. [5, 6]. The PW plasma characteristics would place it within the colored box ”High
Pressure Arcs & Lightning”.

13

Plasmas generally need a continuous source of energy to sustain themselves, as otherwise the

electrons and ions will tend to recombine back into neutral particles. In a star, this energy

source is nuclear fusion. In a laboratory plasma arc such as the PW, the energy source is

the electric field generated by the power supply in combination with the electrons expelled

from the cathode(s) which initiate the process of ionizing the background gas, a process

that propagates down the channel’s length. If the local electric field is sufficient such that

electrons may be emitted from the cathode surface and gain enough energy to ionize the

local gas, electric breakdown will occur and an arc flow of current will be triggered [5]. In

the PW, this high arc-initializing field is generated by means of a Tesla coil, which is only

necessary to initiate the arc and is otherwise inactive. Subsequently, ions produced in the

initial breakdown are heated through collisions with electrons, and are drawn to the cathode

surface by the plasma electric field (separate from the Tesla coil field), whereby collisions

heat up the cathode. The combination of the cathode’s electric field and the heating by ion

bombardment can allow electrons in the cathode to be elevated above the surface’s work

function and be ejected into the plasma. This is thermionic emission and distinguishes arc

discharges from glow discharges, in which electrons are liberated from the cathodes by ions

accelerated through a local potential drop, the cathode sheath [5, 28]. These electrons gain

energy in the electric field that is established in the channel between cathode and anode,

and share that energy with the heavy particles (ions and gas) through elastic and inelastic

collisions [28].

It may spare some confusion to point out that in this thesis the descriptor “heavy” is

applied in two distinct contexts: one referring to accelerated ion beam particles of relatively

high nucleon count e.g. uranium; and a second referring to those particles within a plasma

which aren’t electrons (i.e. the neutral gas and singly-charged ion species). Generally these

14

will be discussed as “heavy ion beam particles” or “heavy particles” for the two situations

respectively, and the context of the discussion should be sufficient to deduce which is being

referred to. The plasma heavy particles are also frequently simply called “heavies”.

An arc discharge is characterized by a moderately high current (I > 1 A) and low

voltage (10s-100s of volts) [28], and a cascaded arc structure is a common means of enclosing

this arc. The cascaded arc structure is a type of wall-stabilized arc discharge in which

there are a series of individual metal plates insulated from one another along the channel

with a floating potential dictated by the plasma within, in between the cathode and anode.

This structure enables a gradual stepping down of voltage between the cathode and anode,

granting greater stability to the arc than would otherwise be achievable over that same

distance [29]. Additionally, this allows for the enclosing surfaces to be water cooled while

not being a grounded surface that the arc would terminate at. Figure 1.9 shows a photo of

such an arrangement, our cascaded arc that we refer to as the plasma window. The structure

of the plasma window will be presented in detail in Section 2.1.

The arc is termed “wall-stabilized” because in order for the arc to be operated continu-

ously, the high heat load (up to tens of kW) is transported via conduction to the walls [28].

This heat must then be removed to a void damage to the material structure, so all of these

components need to be continuously cooled in order to prevent excessive heating, as they

are all in contact with the heated gas of the arc. Pure water is usually the coolant of choice

due to its low cost, ease of implementation, and high specific heat capacity. Furthermore,

pure water (emphasizing that the water must be pure) has low conductivity so there will be

very little electrical current through the coolant.

In Ref. [29] Maecker notes that for arc discharges that are arranged horizontally, as is

the case in the present plasma window, there can be some nonuniformity in properties due

15

Figure 1.9: A photo of the plasma window. Labeled components are as follows: A. are the
cathodes, B. are the cascaded plates (6 total in this image), C. is the anode plate attached
to an expansion chamber connected to the vacuum pump assembly, and D. is the ion beam’s
trajectory through the plasma window, and the direction of gas flow. Outside of this image
on the left side is the GCS chamber.

to natural convection. This effect is not considered in this work as the convective rate is

insignificant compared to the plasma flow speed ranging from 100s to 1000s of m/s.

In the present application, the existence of the arc discharge in a channel connecting a

chamber maintained at high pressure to a low pressure one under continuous evacuation is

used to effect a reduction in the mass flow of gas through the channel from what it would be

without any plasma arc in the region (just gas flow). The most commonly cited mechanism

for being the root cause of this flow rate reduction is an increase in the channel’s viscosity

due to arc heating the gas throughout [30–32] and frequently the mass flow is reported to

be described in terms of Poiseuille’s equation [33–37], given by:

πD4 ¯ρP(cid:48)
128¯η

.

˙mP =

16

(1.3)

Here ˙mP is the Poiseuille mass flow rate, D is the channel diameter, ρ is the mean mass den-
sity of the gas throughout the channel, P(cid:48) is the axial pressure derivative, and η is the mean

viscosity throughout the channel. However, Poiseuille’s equation, which is derived assuming

a near-constant velocity through the channel, does not accurately model the characteristics

of the flow. Viscosity in fact plays only a minor role in establishing the mass flow through

the arc channel. The reasons for this are explored in detail in Section 4.2.6.

The degree of flow reduction achieved depends upon the operating conditions that a

user can impose on the plasma window structure, namely the gas pressure upstream of the

plasma, the arc current passing through the plasma, the geometry of the channel confining

the arc, and the gas(es) flowing through the channel and being ionized. The influence of

each of these properties on the flow rate will be investigated in this work. The limitations

of the arc with reference to these properties will also be explored. Another phenomenon to

note is the existence of a choked flow condition at the exit of the PW, where the gas expands

into a larger chamber. Here the flow speed is supersonic and the pressure in this area can

not have any impact on the behavior within the PW channel itself. Therefore, the flow rate

through the channel for some given GCS pressure and arc current cannot be made any lower

by changing outlet side characteristics.

There are operational limitations associated with each of these features of the arc which

an operator sets. For a given arc current, gas pressure can only be reduced so much, until at

some point there are insufficient ion collisions on the cathode to expel electrons to sustain

the arc current. At this point, the arc collapses. The capabilities of the cooling system

place upper limits on the gas pressure and arc currents, since the heat rate delivered by

the arc to the electrodes increases with both quantities. Voltage drop over the arc increases

with increasing cathode-anode distance (accomplished by employing either thicker plates or

17

more of them). Plasma conductivity needs to be maintained over the entire channel to allow

for electrons to transmit the current across the length, so the electric field must remain

roughly unchanged over a longer distance, thus necessitating a greater total voltage drop

with increasing arc length.

For the flow of any fluid through a region, one can obtain equations describing the balance

of conserved kinetic properties by taking velocity moments of the Boltzmann equation [38–

40]. The Boltzmann equation describes the statistical behavior of particles of species a whose

velocities can be described by a distribution function fa(t, r, v) over positions r and velocities

v. This Boltzmann equation is given by:

∂fa
∂t

+

∂
∂xβ

(vβfa) +

∂
∂vβ

(cid:32)

Faβ
ma

(cid:33)

fa

= Ca ,

(1.4)

in which t is time, β are the spatial dimensions (there is an implicit sum over these in the

above equation), ma the mass of species a, Faβ is the force exerted on a particle of species a

and velocity v, and Ca is called the collision term, which characterizes the effect of collisions

between species and other species, either via elastic or inelastic scattering. We will consider

this being applied to a plasma consisting in part of charged species which interact via the

electromagnetic force involving a particle of charge ea, so:

Fa = eaE + ea(v × B) .

(1.5)

Balance equations for conserved properties (mass, momentum, and energy in particular)

can be obtained in terms of macroscopic characteristics of the plasma by multiplying Eq.

(1.4) by a power of velocity, and integrating over the distribution fa(¯x, t) [39,41] over velocity.

18

Doing so with the v0 = 1, produces the particle continuity equation:

∂na
∂t

+ ∇ · (naua) = Sa ,

(1.6)

where na is the number density of species a, ua is the fluid flow velocity of species a, and Sa

is the source term for volume production of species a.

Integrating over the distribution fa(¯x, t) with v1, specifically multiplying (1.4) by mav,

produces the momentum balance equation:

(mnaua) + nam(ua · ∇)ua + ∇Pa + ∇ · ↔

π − qna(E + (ua × B)) = Sm ,

(1.7)

∂
∂t

in which - in addition to the previously mentioned symbols - ma is the mass, Pa is the partial

pressure, q and is the electric charge, all of species a. Also, the electric field and magnetic

field are given by E and B respectively,

↔
π is the stress tensor, and Sm is the source term for

volume production of momentum for species a.

Integrating over the distribution with the velocity power being 2, specifically multiplying

(1.4) by ma

v2
2 produces the energy balance equation:

(cid:32)

∂
∂t

(cid:33)

+ ∇ ·(cid:16)3

2

3
2

nakTa

(cid:17)

nakTaua

(cid:16)↔
π · ∇(cid:17)

+ nakTa∇ · ua +

u + ∇ · Q = SE ,

(1.8)

in which Ta is the temperature of species a, Q is the thermal heat flux, and SE is the source

term for volume production of energy for species a.

Though these equations may appear daunting in these forms, some simplifying measures

19

will be applied in Section 3.3 to make them more palatable and while still readily useful for

analysis of the plasma window.

1.2.2 Collisions

Collisions in this work are always be treated as binary, between two particles which can

either be the same type or different.

If one of these collision participants is very slow

relative to the other, we consider it stationary. Given that the thermal speeds of electrons
and heavy particles are vastly different whenever Te ≥ Th (which is always the case in the

plasmas investigated here). Due to the vast mass discrepancy, electrons can be considered

as projectiles and heavies the stationary targets. The frequency with which a given binary

collision occurs can be expressed as:

νc = ntar(cid:104)vσ(cid:105) ,

(1.9)

where the collision frequency is given by νc, the electron velocity is v, the target particle

density is ntar, and the process cross section is given by σ. The brackets signify that an

average must be taken over the projectile energy distribution. We assume the velocity

(cid:113) 2E

me

distribution is isotropic so we can substitute v for the kinetic energy

projectile.

of the electron

In general, the electron temperature can be, and frequently is, different from the tem-

perature of the ions or gas. However, the ion temperature and gas temperature (that of the

neutral particles) are frequently considered to be the same and don the moniker heavy parti-

cle temperature, Th. This condition, also sometimes referred to as thermal nonequilibrium,

is established when the electron-heavy energy exchange rate is close to or slower than the

20

time scales for plasma transport [42, 43]. The rate of energy exchange between two identical

particles (electron-electron or heavy-heavy) is much more rapid than the exchange of energy

between electrons and heavies [28, 39, 44] because binary collisions of like-massed particles

results in greater energy exchanged than in collisions between particles with a large mass

disparity. The associated self-thermalization times are quite rapid [41], as can be seen by

the energy exchange rate Qab for species a and b:

Qab = 3

ma
mb

naνabk(Ta − Tb) ,

(1.10)

where the species masses are given by m, temperatures are given by T , and the momentum-

transfer collision frequency between the two is νab. For particles of large mass disparity, e.g.

if electrons colliding with gas atoms, the ma
mb

term will be smaller by a factor of at least

1/2000 than if the colliding species were both electrons or both gas atoms.

1.2.3 Emissions

Energetic electrons colliding with the heavier plasma constituents (ions and neutrals) can do

so either elastically, or inelastically. With sufficient energy, electrons can ionize the heavy

particle, removing one of its valence electrons in a reaction given by:

e + Ai ←→ 2e + Ai+1 ,

(1.11)

where i is the initial ionization stage of atom species A. Note that this is a reversible reaction,

with the reverse process being a three-body recombination. The atom can also undergo an

excitation by the electron-impact collision, where one of the valence electrons is promoted

21

to a higher energy level:

e + Ai(l) ←→ e + Ai(u) ,

(1.12)

where l and u denote lower and upper energy states of the reaction respectively. Note again

that this is a reversible reaction.

Each possible reaction is governed by an interaction cross section, which, when coupled

with the electron velocity distribution function, can be used to obtain that reaction’s rate.

Furthermore, if one assumes that the thermal electron velocites are much larger than any

directional velocities, the three-dimensional Maxwell-Boltzmann distribution can be foregone

in favor of a velocity-magnitude, or electron energy distribution function (EEDF) f (E, Te).

Generally the heavy particles (neutrals and ions) are colder than the electrons, but even

for equal temperatures, the heavies will have much lower thermal speeds due to their larger

mass. As a result, for a given binary electron-impact reaction, the rate constant K of that

reaction can then be obtained by:

f (E, Te)(cid:112)2E/me σ(E)dE .

(1.13)

K =

(cid:90) ∞

0

Here, E is the electron kinetic energy, me the electron mass, σ(E) is the process cross section

as a function of energy, and f (E, Te) is the EEDF which is a function of energy E and the

electron temperature Te.

From here on, this section will refer to excited states as excitations of the neutral species,

but it is worth emphasizing that so long as the heavy particle in question is not completely

ionized (if that’s the case, there are no more electrons to be excited or removed), all of the

following can also apply to an ion’s excited states as well. After being excited, the atom

22

will remain in that state until it undergoes another process - either spontaneous emission

to a lower state, or another collision with an electron that results in another excitation,

de-excitation, or ionization.

In a spontaneous emission, the excited atom relaxes to a lower state by emitting a photon,

which are typically in the infrared, visible, or UV range. This process naturally occurs

in plasmas with predictable rates [7, 45] without any external influence, so utilizing these

emissions for diagnostic purposes is convenient in that it is noninvasive and does not perturb

the plasma [46], unlike other plasma diagnostic tools such as Langmuir probes which create

a local perturbation. The photon energies of these emissions are equal to the difference

between the upper (excited) and lower (relaxed) state. The characteristic energies of these

excited states are linked to the the atom (or ion) in question. A Grotrian diagram indicates

the energy levels of potential excited states of a given element and charge state and the

allowed transitions between them. One example is provided in Fig. 1.10 for excited atomic

helium (or He I) transitions. This diagram shows the emission lines observed in helium

plasma using a spectrometer which will be described in Section 2.1.3.1

There are other sources of light from a plasma as well, which contribute to the spectrum’s

continuum emissions. These are, blackbody, free-bound transitions, and free-free transitions.

In the visible wavelengths which are of concern in this thesis, the primary contributors

are free-bound transitions and free-free transitions. These sources of continuum radiation

originate from interactions of electrons with the heavies, i.e. the neutrals and ions. The

free-bound radiation, also called recombination radiation, originates from a free electron

recombining with an ion to form a bound state of an atom (or ion of a smaller charge state

than originally), resulting in an emission of energy equivalent to the kinetic energy minus

the difference between the ionization energy (corresponding to the original ion) and the

23

Figure 1.10: A Grotrian diagram illustrating the excitation level scheme of He I, with the
levels in orange being the metastable levels. Blue lines indicate observed He I emissions that
will be used to determine electron temperature Te and electron density ne. The labels are
the emission wavelengths in nm.

24

bound state energy. Free-free radiation, also called Bremmsstrahlung radiation, results from

acceleration of electrons colliding with an atom or ion, but without involving a recombination

(the electron remains free after the interaction) [7, 47, 48].

1.2.4 Equilibrium Types

Often, the electrons within a plasma are assumed to follow a Maxwell-Boltzmann distribu-

tion, particularly at electron densities exceeding 1015 cm-3, as is the case for the PW. This

claim will be examined in more detail in Section 3.1, but for now we will take the electron

energy distribution function (EEDF) as a Maxwellian, given by:

(cid:33)3/2

(cid:114)

(cid:32)

E
π

1
kTe

(cid:32)−E

(cid:33)

kTe

f (E, Te) = 2

exp

,

(1.14)

in which E is the electron energy and Te is the electron effective temperature (an average

quantity over the energy distribution function)

Practically, it is frequently of great importance to be able to calculate relative populations

of the excited states of atoms or ions in a plasma of some temperature, pressure, and electron

density, and doing so requires knowledge of the EEDF. All processes are in equilibrium

with the inverse process, including emitted de-excitation radiation and its absorption. The

populations of these excited states also depend upon the class of equilibrium the plasma

exists in. Some relevant equilibria are briefly introduced below.

Thermal Equilibrium: This is a generally un-achievable condition in which particle

densities can be calculated for all excited states, and are given by Boltzmann relation [43]:

(cid:33)

nk
nj

=

gk
gj

exp

− Ek − Ej

kT

(cid:32)

25

,

(1.15)

in which, for states j and k, n are the state densities, g are state degeneracies, and Eu are

the state energies.

Local Thermodynamic Equilibrium:

In the local thermodynamic equilibrium (LTE) regime, all kinetic temperatures are lo-

cally equal for each particle species, so Te = Th = T [44,49]. Rates from collisional processes

are much greater than rates from radiative processes , and all excited levels are in a ther-

modynamic equilibrium system of the same temperature T , so level densities are given by

a Boltzmann distribution as in Eq. (1.15). This condition can sometimes be satisfied in
laboratory plasmas, but requires relatively high densities, generally around 1 × 1017 cm-3 at

least [47, 50].

Partial Local Thermodynamic Equilibrium:

In this case, only populations of excited levels of sufficiently high state energy are re-

lated via Saha-Boltzmann relations to the next ionization stage’s ground state. Equations

and further discussion on the topic of partial local thermodynamic equilibrium (PLTE) are

presented in Section 2.2.3.1.

1.3 Dissertation Organization

Chapter 2 — Experimental outlines, design, and instrumentation of the NSCL plasma win-

dow test stand will be described in this chapter.

Chapter 3 — Theory governing operation of the cascaded arc and flow characteristics in

the plasma window as well as models with which to compare measurements with will be

discussed.

Chapter 4 — Analysis results will be thoroughly detailed for the plasma window operating

26

conditions that have been studied, and comparisons with other works will be presented.

Chapter 5 — Key findings will be summarized and discussion of the subsequent necessary

steps for implementation with a gas charge stripper will be given.

27

Chapter 2

Experiment

2.1 Test Stand

Many of the components of the NSCL plasma window test stand have previously been de-

scribed in Ref. [51]. The plasma window portion of the test stand is shown in Fig. 2.1,

showing its position between the GCS chamber and the main chamber, also called the ex-

pansion chamber. The test stand acts as one side of the gas charge stripper assembly through

which the ion beam would traverse. The system can be operated in either a fresh-gas mode

in which the gas flow is sustained from a gas cylinder and is expelled directly to atmosphere,

or in a recirculation-mode in which initially a large buffer chamber is pressurized with the

gas from the cylinder and once full, a series of valves change the flow origin from the gas

cylinder to this buffer chamber. In this mode, the gas is not expelled to atmosphere and

instead continuously cycles through the test stand. Schematic diagrams for the fresh gas

mode and recirculation mode are presented in Figs 2.2 and 2.3 respectively.

The gas flow is measured via an OMEGA FMA 1844A flowmeter calibrated for helium

flows from 0 to 500 SLM. If the gas is argon, then a relative correction factor can be ap-

plied to convert between the measurement to equivalent argon flow according to instrument

documentation. This relative correction factor, given in the respective device manuals, is

expressed as:

28

Figure 2.1: A photo of the test stand, showing the section that includes the plasma window
and associated diagnostics, the gas charge stripper chamber, and the main chamber.

Figure 2.2: Plasma window test stand schematic in fresh gas flow mode. Either argon or
helium is introduced via the gas cylinder feed.

29

Figure 2.3: Plasma window test stand schematic in recirculation gas flow mode. Before
operation, the buffer chamber is pressurized to around 12 PSI.

30

Krel =

Ka
Kb

,

(2.1)

where Ka and Kb are the correction factors in translating from a nitrogen-calibrated in-

strument to flow in gas a and b respectively. The instrument documentation provides that

KAr = 1.205 and KHe = 2.43.

2.1.1 Plasma Window

The gas that ionizes to plasma inside the plasma window is that which flows out of the GCS as

a result of the pressure difference established between the GCS and the main chamber which

is attached to the vacuum pumps. The high pressure GCS chamber is located upstream of the

cathode-side of the plasma window, and the anode-side being attached to the low pressure

main chamber. A voltage of -300 V is applied between the PW and the GCS, in a small

region separated on either side by insulating breaks, in order to prevent stray electrons from

creating an arc backwards to the grounded GCS, a scenario that can be highly damaging

to the metal tubing in this region. This feature is illustrated in Fig. 2.4. The region then,

going upstream to downstream, contains the following each separated by insulating breaks:

grounded GCS, the anti-backwards-arcing voltage, and the cathode housing structure of the

PW.

As indicated in Figs. 2.2 and 2.3, the gas flow from the either the pressurized gas cylinders

or the buffer chamber (depending on operation mode) is adjusted either automatically with

an MKS 250E pressure/flow controller or manually with a manual bypass valve so as to

obtain the desired pressure in the GCS, monitored by an MKS Baratron 622B. A photo of

the plasma window is shown in Fig. 1.9 as set up for a 6x6mm configuration. Another view,

31

Figure 2.4: A photo of the region between GCS (shown on left side) and PW (out of view
on right side). A voltage supply maintains a -300 V relative to the GCS in order to repel
electrons that would generate an arc upstream towards the GCS rather than downstream
through the PW.

this time for a 8x6mm configuration is shown in 2.5, this time showing some of the primary

diagnostics used throughout this work.

The plasma window consists primarily of a cathode side and a set of individually insulated

metal plates of floating potential which gradually step down the plasmas potential to the

final grounded anode plate. These metal plates are what give this arc structure its name:

cascaded arc. These wall voltages are established as follows: within the plasma, diffusion

of the charged particles results in a portion of them colliding with walls of the channel.

However, due to their vastly different masses and speeds, electrons and ions will collide with

32

Figure 2.5: A photo showing another plasma window configuration, this time being a 8x6mm
configuration and including several diagnostics used in characterizing the plasma. A. is the
gas inlet connected to GCS, B. is one of the three cathodes inserted into the channel, C.
are the PW cascaded plates, D. are copper fingers connected to voltage measurement setup
described in Section 2.1.3.3, E. is the anode plate, and F. are diagnostic plates.

33

Figure 2.6: A photo of the components between PW plates and a bare plate. The labels are
as follows: A. is the FR4 insulator, B. is the FFKM o-ring, C. is the alumina inner insulator,
D. is the inner copper surface, E. is the plasma channel, and F. are the water coolant entry
and exit ports. The top photo is of a cross sectional view of the plate, showing the coolant
channel position and size.

the walls at different rates. For an electrode that is floating with respect to the plasma, this

will result in a potential that is negative with respect to the bulk plasma potential.

Figure 2.6 illustrates the design of the plates and the components between the plates.

34

The plates are separated by a trio of concentric ring pieces: innermost is a ceramic insulator

that protects the FFKM o-ring which is the middle component, and outermost is an FR4

insulating piece. These three ringed pieces provide insulation between plates so that their

floating voltage and heat load can respectively be measured at multiple locations down

the DC arcs channel in addition to allowing good vacuum sealing throughout the structure.

Throughout this project, several different ceramic insulator materials have been used: boron-

nitride (BN3), aluminum-nitride (AlN), and alumina (Al2O3). Each plate has a channel for

water coolant to pass surrounding the inner bore where the plasma is contained. Water of

known flow rate and known supply and return temperatures is used as coolant, enabling one

to easily calculate the amount of power removed for each plate via calorimetric analysis. The

unique diagnostic plates that will be discussed in detail in Section 2.1.2 are made entirely

of copper, whereas the other ordinary plates are comprised of a copper inner piece that is

electron beam welded to a stainless steel outer piece.

The cathode segment consists of a holder which has three holes at azimuthally separated

by 120 degrees, and at 30 degrees out from the longitudinal axis (arc-axis). The structure

of the cathode holder is shown in Fig. 2.7. The cathode holder is a copper tube with an

inner pathway to allow for water coolant similar to with the plates. Outside of this is a

2-piece insulating collar. The base part of this is a Vespel insulator (labeled C in Fig. 2.7)

and functions as a spacer between the conducting metal of the electrode, and the housing

structure (H). The other part is a hollow cylindrical jacket (B) that sits atop the Vespel

base and extends along the remainder of the copper electrode piece (F). Additionally, an

FFKM o-ring (D) is fitted on the outside of this insulator to provide vacuum sealing against

the lip of the housing hole into which the cathode is inserted. Screwed into the top of this

copper is a wide copper attachment called a shield in which is held the thoriated tungsten,

35

Figure 2.7: A photo showing the components of the plasma window’s cathode structures.
A is the W-ThO2 cathode tip, B an alumina jacket, C a Vespel insulator, D a FFKM o-ring,
E a nut to affix the structure to the housing, F the water-cooled copper holder, G the water
inlet and outlet, and H the cathode housing.

W-ThO2 cathode tip (A). The thoria is about 2% by mass. The thoriated tungsten cathode

itself is a cone-tipped rod, 2.4 mm in diameter ending in a sharp tip whose conical full-angle

is 30 degrees. The exposed cathode tip emerges 6.0 mm out of the copper shield. The W-

ThO2 tips are manufactured to be long enough to extend out the back of the shield by the

threading, so that after some period of usage it may be pushed through and re-machined to

get back to a clean surface of the dimensions shown in Fig. 2.8.

2.1.2 Procedure

The arc is always initiated in the fresh gas flow mode schematically represented in Fig. 2.2.

This is done by opening the valves to maintain a constant, low flow in argon gas. If our

ultimately desired gas to study is helium, we still initialize in argon as we have had very

36

Figure 2.8: A photo indicating the dimensions of the exposed 2% by mass W-ThO2 cathode
tip inside the copper shield. This is a zoomed view of component A in Fig. 2.7.

little success in initializing the arc directly from helium and attempts usually resulted a spark

generates in the opposite direction, from cathode backwards to the GCS, which can cause

damage to other hardware. While keeping the gas flow relatively low (around 5 SLM), the

arc is initiated using an Electro-Technic Products BD-10A Tesla coil (20 kV). This provides

a large electric field, enabling an initial expulsion of electrons from the cathode in a field-

emission regime. These electrons then ionize gas which are accelerated back to the cathode

and heat it up, until a thermionic emission regime is reached. The arc then heats the gas,

which effectively acts to partially plug the flow and causing the cathode-side pressure to

increase, such that the emission regime transitions to thermal emission. This process occurs

in a short enough duration that the Tesla coil need only be active for a fraction of a second.

This is controlled via a foot-operated switch.

37

Figure 2.9: A drawing of the PW and part of the Main Chamber. The cone is also shown
which acts as a heat sink for the hot plasma in the main chamber.

The anode plate is sealed against a large expansion chamber (referred to as the main

chamber) with a Viton o-ring. This chamber has water cooling channels on several of its

faces, and is grounded. Within the main chamber is a grounded structure referred to as the

cone which is shown in Figs. 2.9 and 2.10, which much of the hot gas exiting the plasma

window channel impinges upon, so this cone acts as a heat sink and so also is water cooled.

Attached to the main chamber is a sapphire glass viewport, a Granville-Phillips series 275

Mini-Convectron, and a large conductance (about 25 cm diameter) bellows which connects

to a Edwards EH4200 Booster Pump and Edwards GV400 mechanical pump in series, which

then exhausts in standard operation to atmosphere through a Varian Scroll pump. However,

as mentioned earlier, this system can also be operated in a recirculation mode which is laid

out in Fig. 2.3. This is transitioned to from the standard exhaust mode by closing off the

scroll pump pathway whilst simultaneously opening a recirculation pathway. In recirculation

38

Figure 2.10: A photo looking through the viewport of the main chamber. The cone is
visible, being bathed in the argon plasma exiting the PW.

mode, the gas feed is a large buffer chamber, shown in Fig. 2.12, rather than a gas cylinder.

The gas flow rate is controlled by the parallel pairing of remote control and manual valve,

then the gas passes through the GCS where static pressure is measured via an MKS Baratron

622B before flowing downstream back through the plasma window. This recirculation mode

is of crucial importance for the plasma windows use with a gas charge stripper because the

high degree of gas flow would otherwise rapidly deplete the reserve of gas feeding the device,

becoming very expensive and wasteful.

The plasma window is sustained via the three cathodes, each of which are connected

to two Sorensen SGA power supplies (400 V and 38 A limits each), for a total of 6 power

supplies and a current limit of about 225 A. The full plasma window circuit as shown in

Fig. 2.11 includes also an inductor-resistor series (1 mH at 100 A DC and 1 Ω respectively),

39

Figure 2.11: A diagram showing the plasma window circuit. Pairs of PW power supplies are
in series with inductors and water cooled resistors to provide stability to voltage fluctuations.
Three of these sets are in parallel, leading to the PW load.

Figure 2.12: A photo of the gas-feed components of the PW. The GCS chamber can be
partly seen in the top left corner of the photo, and the PW is even farther left (out of view
here).

40

one per cathode, which provide stability to the arc since any transient behavior of voltage

fluctuations is spread out in time as a result of the large time constant L/R of the series.

Because the power dissipated through these resistors at currents of up to 70 A (per resistor),

is quite large, they must be water-cooled. These power supplies are operated in current

mode, the cathodes themselves being at floating voltage with the plasma, generally between

100 and 200 V. So, one of the primary controls of operating conditions will be the plasma

window arc current.

The structure of the plasma window and the plates that comprise it has already been

discussed, but a select few plates were manufactured with an additional feature. These,

referred to as diagnostic plates, have a hole between the supply and return of the water

coolant path, drilled down to the central bore, giving diagnostic access to the plasma at

that plates location along the plasma window channel. This is then outfitted with an MKS

Baratron 727A pressure gauge to determine the gas static pressure at that plates location,

and a fiber optic feedthrough with a collimating lens for greater light acceptance, all of

which can be seen in Fig. 2.13. In addition to fiber optic feedthroughs to receive the plasma

emissions at the diagnostic plate locations, there is a fiber optic feedthrough positioned along

the central axis (arc axis) at both the end of the CGS and the end of the Main Chamber.

This provides a vantage point along the entire length of the arc from both the cathode-side

(Front) and the anode-side (Back).

There are several notations regarding the arrangement of these plates in the PW that

will be used extensively throughout this dissertation. One of the goals of this study is to

examine the differences between arc performance in various different arrangements of plates,

hereafter referred to as PW configurations. These are identified based on the number of them

at specified aperture sizes as in the following examples: 8x6mm is a configuration consisting

41

Figure 2.13: A photo indicating the setup of the diagnostic plate. The copper diagnostic
plate itself can be seen positioned at P2/6 here. The diagnostic plate’s fiber optic feedthrough
and pressure sensor are also visible on the outward side of the diagnostic arm which is
grounded. An insulating break separates this grounded side from the floating voltage of the
plate.

42

Figure 2.14: Cross sectional diagram of the plasma window and the primary components
which comprise it . The insulating components and o-rings between the plates are shown in
Fig. 2.6, and the cathode components are shown in Figs. 2.7 and 2.8.

of eight 6 mm aperture plates, while 1x6mm 7x10mm is a configuration consisting of one 6

mm aperture plate followed by seven 10 mm aperture plates. Reading the notation left to

right translates to the plate arrangement from cathode to anode. The notation to refer to

the diagnostic plate locations will be as in the following examples: P2/8 refers to plate 2 out

of a total of 8 in that particular configuration.

2.1.3 Diagnostics

2.1.3.1 Spectrometer Characteristics

Calculations from the spectral measurements at these locations comprise a significant por-

tion of the analysis conducted in characterizing the plasma within the plasma window as

a function of operational conditions (pressure and arc current). This light is acquired by

43

connecting fiber optic cables from the optical feedthroughs at the aforementioned locations,

directly to an Ocean Optics HR4000. The spectra are displayed as spectral irradiance, with

the abscissa being wavelength λ. This instrument has a 5 m wide entrance slit, a grating of

1800 lines/mm, calibrated for relative irradiance acquisitions. This calibration is performed

using a bare-fiber viewing a StellarNet SL-1 2800K blackbody lamp, shielded from ambient

light. This is the reference spectrum and will correct for the spectrometer’s instrumental

response function over the wavelength range.

A dark spectrum is also required. To minimize contribution of noise, both of these steps

in the calibration process are performed by averaging a large number of consecutive scans.

During long-duration operation, the spectrometer may require subsequent dark calibrations

due to changes in ambient temperature causing small perturbations to light collection, caus-

ing the dark and reference calibrations potentially to drift. The used to obtain the relative

irradiance calibration is:

Iλ,T = Bλ,T

Sλ − Dλ
Rλ − Dλ

,

(2.2)

where Iλ,T is the calibrated relative irradiance at wavelength λ, and Sλ, Dλ, and Rλ are the

sample spectrum (from the plasma in this case), the dark spectrum, and the blackbody lamp

reference spectrum respectively at the corresponding wavelength and each given as counts.

Bλ,T is the function representing a blackbody’s irradiance spectrum at a temperature corre-

sponding to that of the blackbody lamp used for the reference spectrum. This is computed

from Planck’s law:

Bλ,T =

2hc2

exp(hc/λkT ) − 1

.

(2.3)

44

The intensity of emissions from the plasma window varies dramatically with operating

conditions and observing location, so this calibration procedure must be performed with a

range of different collection integration times from 15 ms to 10 s. A more reliable, though

more complicated calibration could be performed using an intensity-calibrated standard,

allowing us not only to not need to rely on the assumption that the blackbody lamp does

indeed accurately replicate a blackbody of 2800 K, but also enables calculations of excited

state densities and more reliable electron density measurements [46, 47, 52]. This was not

employed for the present plasma window work.

2.1.3.2 Coolant Calorimetry

Water coolant temperatures are measured at locations both upstream and downstream of

the hot component which it cools. The arrangement of coolant primary manifolds is one

for each of the following sections of the test stand: the mechanical and booster vacuum

pumps, the main chamber and the three 1 Ω resistors, and the cone structure. Additionally

there are two primary manifolds dedicated to the plasma window structure itself. The Fluid

Chillers WAT30000 chiller which pumps and cools the water flowing through the entire PW

test stand is rated for 30 kW, and its cooling functionality is generally active for a period of

several minutes followed by a cooling-inactive period of several minutes (though the water

coolant is pumped at all times). Pure water is used because of its relatively large resistivity

which limits the electrical current leaked through the water to ground.

The water flow rate in each of these primary manifolds is measured using liquid flow

monitors by Universal Flow Monitors, rated for 0 to 5 GPM. All of the components (cathodes

and plates) in the plasma window have a single coolant path, the only exception being the

cathode holder which has two coolant paths. The coolant flow rate through each of these

45

paths is determined simply as 1/N with N being the total number of coolant paths connected

to that manifold. The power which is removed by the coolant is determined calorimetrically

using:

Hw = cp ˙mc∆T ,

(2.4)

where Hw is the power into the wall, cp is the specific heat of water (4.184 kJ/kg*K), ˙mc is

the coolant mass flow for that component, and ∆T is the difference in measured temperature

from upstream and downstream of the plasma window component. Because the plasma is in

a steady state, the power that is cooled equals the power with which the plasma heats the

given component of the plasma window.

To properly make use of Eq.

(2.4), one must also subtract out the null values that

one reads for temperature difference of the temperatures down and upstream of the PW

without any arc presence. This is done in two steps in this work: a chiller cycle null value

is taken as the difference between the down and upstream temperature sensors (for a given

PW component) over a time in which the chiller is active but the arc is not. Similarly, an

ambient null value for the temperature difference is taken as the difference between down and

upstream temperature sensors over a time in which both the chiller and the arc are inactive.

This ideally is taken very close in time to the actual experiment. Sample acquisitions for

both of these are illustrated in Fig. 2.15.

The corresponding temperature corrections from each of these null values are given simply

by:

∆Tnull,j = Tin − Tj|nulltype .

(2.5)

46

Figure 2.15: Sample acquisitions of both ambient null (left) and chiller cycle null temperature
values.

Using this, one would replace the ∆T in Eq. (2.4) with ∆T−∆Tnull,j for each PW component

j, and taking the sum of the ambient and chiller cycle null values.

2.1.3.3 Plate Floating Voltages

A critical property of an arc plasma that dictates the dynamics within is the electric field

that is sustained between the cathode side and the anode side.

In a DC cascaded arc,

the axial component of the electric field is taken to be approximately constant across a

given cross-sectional area of the channel. This electric field can be determined at discrete

locations along the channel axis of the plasma window by measuring the floating voltage of

each plates enclosing the plasma and taking the gradient along the direction of the channel

47

01020304022.022.122.222.322.422.522.622.722.822.923.0010203040101214161820Component Temperature [C]Time [min] PWInlet Temp PW Plate 1 Temp PW Plate 3 TempAmbient NullsChiller Cycle NullsTime [min]axis. This electric field is taken to be located at the midpoint between the adjacent plates

whose voltages determined the local gradient. It should be stressed that it is assumed that

the electric field in the bulk of the plasma is about the same in magnitude as that determined

by this method from wall voltages.

The system used to measure the PW floating plate voltages consists of a G10 insulator

platform positioned near the PW plates, and attached to it are copper fingers - one per plate

and another for the cathode housing - connected to a voltmeter through a rotary switch. The

switch is controlled with a G10 insulator rod so that each plate voltage can be measured.

Components of this plate voltage measurement system can be seen in Figs. 2.5 and 2.13.

2.2 Optical Emission Spectroscopy

2.2.1 Introduction

Plasmas generally emit radiation across much of the electromagnetic spectrum and through

a variety of mechanisms. Most important for the present work is intra-excited-state de-

excitation processes which emit characteristic radiation. Wavelengths depend on the emit-

ting species and the population of excited levels, while line shapes and relative emission

irradiances depend on plasma properties such as electron temperature Te and density ne.

The primary tool used in this study to characterize the plasma via these line emissions

is a spectrometer which is described in detail in Section 2.1.3.1. Light from the plasma

is directed to this instrument via fiber optic cables and is interpreted as an irradiance-

wavelength spectrum. This is worth explicitly pointing out because quantitative units of light

flux are historically suffered from much ambiguity and name changes, generating confusion

which is hopefully minimized here. Ref. [7] has an effective description which helps to dispel

48

Figure 2.16: Sample spectra obtained from a 6x6mm PW, the vantage point being across
a diagnostic plate positioned at P6/6. The spectra were collected with integration times of
800 ms and 50 ms for helium and argon respectively.

this confusion, but here it will be sufficient to just mention that irradiance, which is the

property measured in this work, is a radiant power W (in Watts) impinging on a collection

area A (in m2). What is collected via the spectrometer is actually a spectral irradiance Is,

so is instead in units of W/m2/nm, so to determine the overall irradiance I of an emission

peak, the spectral irradiance must be integrated over the peak’s wavelength extent. Sample

spectra that represent typical collections are shown in Fig. 2.16 for a 6x6mm PW, for both

argon and helium. These were collected via a diagnostic plate at P6/6 It should be noted

that the emission irradiances between the two gases are quite different, with helium generally

emitting weaker light in the range of the spectrometer (about 385 to 515 nm), and so different

integration times of light collection are required.

49

390405420435450465480495510010203040506005101520253035Irradiance [a.u.]Wavelength [nm]Argon (200 torr 150 A)Integration Time = 50 ms Irradiance [a.u.]Helium (150 torr 150 A)Integration Time = 800 msIn the energy regime relevant for the PW, the primary mechanism for excitation is by

collisions with electrons rather than other heavy particles. This is because not only do

the electrons generally have significantly higher energy than the heavy particles, but also

electron-heavy collisions are much more frequent than heavy-heavy collisions. In plasmas of

densities similar to those in the PW, it is likely that a significant portion of the population

of the higher excited states arises from intra-excitation, or excitation to a higher energy level

from a metastable or other already excited state. Particularly important are excitations from

metastable states which are relatively low-lying excited states that do not readily decay back

to the ground state due to selection rules preventing the transition. Ordinary excited states

of a neutral or lowly-ionized ion may have lifetimes of just a few nanoseconds but that of

metastables can be greater than milliseconds, up to seconds [53]. The relatively long lifetime

of these states and their closer proximity in terms of energy to the higher excited states

than the ground state mean that they can play a significant role in establishing the degree

of ionization of the plasma.

To assess the relative importance of electron-impact excitations and ionizations from these

metastable states compared to from the ground state, rate coefficients have been calculated

for conditions similar to those measured in the PW for argon and helium, i.e. that Te = 1.5

in argon and Te = 2.1 in helium. These coefficients were calculated assuming a Maxwellian

EEDF, an assumption further investigated in Section 3.1. Differential rate constant (DRC)

values are calculated for ionization and excitation from both ground and metastable states

using Eq. (1.13). This is therefore given by:

DRC(E, Te) = f (E, Te)(cid:112)2E/me σ(E) ,

(2.6)

50

Figure 2.17: Differential rate constant for electron-impact ionization from the lowest-lying
metastable level as well as directly from ground level, for both argon and helium. The argon
test case has Te = 1.5 eV and the helium has Te = 2.1 eV.

in which E is the electron energy, Te the electron temperature, f (E, Te) the Maxwellian

EEDF value, and σ(E) is the relevant electron-impact ionization or excitation cross section.

For ionization, a test case of this DRC(E, Te) as a function of the impacting electron’s

energy is shown in Fig. 2.17, using cross sections from Ref. [54] for argon and helium

ionization from ground as well as argon ionization from the metastable, while the cross

section for helium ionization from the metastable is obtained from Ref. [55]. Analogous

plots for excitation are shown in 2.18. For both gases, the metastable is the lowest-lying

excited state, which is identified in the figure. Results are summarized in Table 2.1. The

51

05101520253035401E-231E-221E-211E-201E-191E-181E-171E-161E-151E-140510152025301E-231E-221E-211E-201E-191E-181E-171E-161E-151E-14Differential Rate Constant [m3/s*eV]Electron Energy [eV] Ionization from metastable Ionization from grdHeliumMetastable = 2s 3S 1Metastable = 4s [3/2]' 2ArgonElectron Energy [eV]Figure 2.18: Similar to Fig. 2.17 but for excitation, this is the differential rate constant for
electron-impacts to the lowest-lying metastable level as well as directly from ground level,
for both argon and helium. The argon test case has Te = 1.5 eV and the helium has Te = 2.1
eV. The upper level is 5p [3/2]1 for argon and 4d 3D for helium.

cells highlighted in grey characterize the relative importance of excitations from metastable

states. These, the ratio of rate constants (metastable / ground) represent the required ratio

of densities (again metastable / ground) for the excitation or ionization rates from ground

and from metastable to be equivalent. Relative metastable densities that exceed that ratio

would imply ionization from the metastables is in fact the dominant ionization mechanism.

52

05101520253035401E-231E-221E-211E-201E-191E-181E-171E-161E-151E-140510152025301E-231E-221E-211E-201E-191E-181E-171E-161E-151E-14Differential Rate Constant [m3/s*eV]Electron Energy [eV] Excitation from metastable Excitation from grdHeliumMetastable = 2s 3S 1Metastable = 4s [3/2]' 2ArgonElectron Energy [eV]Table 2.1: Comparison of electron-impact ionization rates from ground and metastable levels
in Ar and He. All rate coefficients are in [m3/s].

Process

Helium

Argon

To excited state 4d 3D To excited state 5p[3/2] 1

Excitation to an emitting state

Excitation from ground

Excitation from metastable

Excitation Rate Constant Ratio

Ionization from ground

Ionization from metastable

Ionization Rate Constant Ratio

8.2 × 10−22 [m3/s]
2.1 × 10−15 [m3/s]

3.9 × 10−7

2.8 × 10−20 [m3/s]
1.4 × 10−14 [m3/s]

1.9 × 10−6

1.5 × 10−20 [m3/s]
1.4 × 10−16 [m3/s]

1.1 × 10−4

5.9 × 10−19 [m3/s]
7.0 × 10−15 [m3/s]

8.4 × 10−5

2.2.2 Electron Density - Stark Broadening

A plasma’s electron density (also often simply called plasma density) is one of the key

properties of a plasma which dictates its behavior and so is a good basis of comparison

between different plasmas, or between a plasma and a corresponding model describing that

system. The electron density dictates the rate at which the heavy particles are heated, which

in turn impacts the mass flow through the arc as will be discussed in Section 3.3. Calculating

this electron density can be performed via several different techniques and instruments such

as Langmuir probes [56], laser interferrometry [57], Thomson laser scattering [58, 59] or

optical emission spectroscopy (OES) [7, 38, 60].

Langmuir probes have the benefit of being able to determine a wider variety of other

plasma properties that cannot be obtained by the other methods, however they can perturb

the plasma locally, and in high pressure arcs their implementation suffers the added challenge

of surviving in the dense and hot environment [61, 62]. Laser interferrometry and Thomson

scattering can provide a higher accuracy measure of electron density as well as excellent

spatial and temporal resolution [63], but requires a more complicated apparatus of laser and

optics providing line of sight into the plasma, the plasma system itself, and a spectrometer

which also must have line of sight into the plasma, to capture the effect of the laser for

53

analysis. This also can perturb the plasma at the location where the laser is interacting

with it. It is also likely that there is a low-density plasma along the length of the diagnostic

channel that cuts through the diagnostic plate which could also emit radiation, though it

is expected to be vastly dimmer than the plasma in the center of the arc, so we summarily

exclude any effect from this.

On the other hand, optical emission spectroscopy has the benefit of being a non-invasive

technique which makes use of the emission from atomic de-excitations. In the PW system,

the diagnostic plate’s optical line of sight is the central chord of the plasma channel at the

specified plate location. The entry of this to the PW channel can cause a local perturbation

to the plasma though it is expected to be minimal.

Broadly there are three physical processes that give rise to broadening of a spectral line,

not including the effect of the instrument itself: natural broadening related to the emitting

state’s lifetime, Doppler broadening originating from the speed of moving emitters, and

broadening resulting from interactions with other particles in the emitter’s vicinity [7]. These

mechanisms will be explored in minor detail here with references providing more elaboration,

with the exception of Stark broadening which will receive a more detailed explanation here.

This broadening originates from the interaction of the emitter with local electrons and ions.

Before attempting to make use of this phenomena to calculate electron density, it is nec-

essary to briefly present the other mechanisms by which an emission line can be broadened.

Rather than being an infinitesimally narrow line, every emission has a natural linewidth,

owing to the finite decay time of the excited state and a corresponding energy uncertainty as

necessitated by the Heisenberg uncertainty principle [52,64]. This linewidth is almost always

several orders of magnitude finer than the others discussed here [47]. Brief explanations and

relative broadening values will be calculated for conditions typical of those in the PW for

54

the following broadening types in addition to Stark broadening:

1. Natural line broadening

2. Doppler broadening

3. Van der Waals broadening

4. Instrumental broadening

Doppler broadening occurs due to the random thermal motion of emitters, which then

contributes red-shifting or blue-shifting of the emission; when including the effects of the

random motion of a collection of emitters, the result is a Gaussian broadening of the emission

line. Because the degree of Doppler broadening is related to the amount of thermal motion

in the emitters, it is frequently used as a means of calculating a temperature of the emitters

(gas temperature if the emissions are from excited neutrals). Doppler broadening takes the

form [7]:

(cid:114)

2kT ln2

M

,

δλD
λ

=

2
c

(2.7)

in which T is the temperature of the emitting species, c the speed of light, and M is the

mass of the emitting species.

The Doppler full-width-at-half-maximum (FWHM) to emission wavelength ratio

δλD
λ , or

relative broadening degree, is inversely proportional to the square root of the mass, so the

effect will be more pronounced for helium than it is for argon. For a helium gas temperature

of 3 eV (this is much higher than what is actually the case in the plasma window, so gives a

far upper bound of expected broadening), this corresponds to a relative broadening degree

of 2.1x10-5. If this is significant relative to the other forms of broadening in the system, then

55

Table 2.2: Approximate relative line broadening degrees (∆λ/λ) for various mechanisms, for
emissions in visible wavelengths. In argon, Te ≈ 1.5 eV, Tg ≈ 1.5 eV, and ne ≈ 2 × 1016
cm-3. In helium, Te ≈ 2.5 eV, Tg ≈ 1.5 eV, and ne ≈ 2 × 1015 cm-3.

Relative Broadening (Ar I) Relative Broadening (He I)

Mechanism

Stark

Doppler

Natural

Van der Waals

Instrumental

1 × 10−4
1.5 × 10−5
2 × 10−7
3.7 × 10−7
1 × 10−4

2 × 10−4
6.6 × 10−5
2 × 10−6
3.5 × 10−7
1 × 10−4

it must be considered, but if it’s smaller than other contributions, it may be ignored. This

will be explored after defining the other broadening mechanisms.

Another broadening type is Van der Waals broadening, a form of pressure broadening

resulting from the dipole interaction of an excited atom with the induced dipole of a neutral

atom [64]. The analysis of this form of broadening requires knowledge of the interatomic

potentials, and a complete treatment can be found in Ref. [7], Ref. [65], or Ref. [64]. Following

those works, the Van der Waals relative broadening from of a neutral emitter from same-

species neutral perturbers, or the FWHM to emission wavelength ratio, can be expressed

as:

= 8.18 × 10−19λ(αp ¯R2)2/5

δλV
λ

(cid:33)3/10

(cid:32)

Th
µ

ng .

(2.8)

In this expression, wavelength λ is in nm, and atomic polarizability αp and neutral density

ng are both in cm-3. Also in this expression, µ is the reduced mass of the emitter-perturber

system in atomic mass units. Lastly, ¯R2 is the difference of the square radius of the emitting

atom’s upper and lower levels, given in units of Bohr radii.

Finally, the instrument with which the emission spectrum is collected also contributes a

degree of broadening to the emission, though this type has nothing to do with the plasma’s

56

properties. In the case of the spectrometer used in this work, an Ocean Optics HR4000 as

described in Section 2.1.3.1, this turns out to be the dominant non-Stark contribution to the

observed line shape and will be discussed in detail below.

Stark broadening analysis is a very commonly employed diagnostic used to ascertain the

electron density of the emitting plasma. We begin with a conceptual description of Stark

broadening. The degree of Stark broadening depends on two general factors: the local plasma

environment and the atomic structure of the emitter, be it atom or ion [64]. Emitting atoms

experience collisions with electrons in the plasma, whose local electric field [8, 66] perturbs

the excited energy levels. This field is often referred to as the microfield, and is the field

distribution inside the screening distance described in section 1.2, the Debye length of Eq.

(1.2). At distances from a charged particle inside of the Debye, quasineutrality doesn’t apply,

hence strong fields may be present [67] at these small distances. In the theory discussed here,

the microfield distribution are presented in terms of what is known as the Holtsmark field

strength [66, 68] which is approximately the electric field strength generated at a the mean

ion-ion separation distance and given in Eq. (2.10). Elaboration and equations pertaining

to this are introduced in subsequent pages.

The perturbation from a projectile impinging on an emitter (an atom or an ion) is

illustrated in Fig. 2.19. In a collision in which an emitter and a charged perturber particle

(e.g. an electron) are separated by a distance R, their separation would start at a large

distance then approach a minimum value (the impact parameter) before increasing to a

large distance again as the perturber recedes. When many emitters encounter such collisions

over a distribution of projectile energies and impact parameters, this perturbation ultimately

manifests as a broadening and shifting of the emission peak profile. Additionally there is a

contribution from collisions between the emitter and ions, which produce an asymmetry in

57

Figure 2.19: Reproduction of figure published in Ref. [7]. This qualitatively illustrates the
perturbations of two energy states originally of energy E1 and E2 as a function of charged
perturber distance R from the emitter. The perturbed energies V1 and V2 set the emitted
photon energy hν. Perturber particle is denoted as P e and emitter particle as Em.

the emission profile.

In working towards a mathematical expression for the Stark-broadened profile, there

are a number of theoretical approaches determining the effect of emitter-charged-neighbor

interactions on a line profile and how to utilize it in assessing electron density. Ref. [69]

provides a nice review of these theories, while Ref. [66] provides a far more in-depth dive

into one of these theoretical approaches, the same that will be utilized in this thesis. A decent

starting point in establishing a theoretical framework for Stark broadening is the spectral

power of one of these spontaneous electric dipole emissions from a single quantum-mechanical

system. This is the point where Griem [66] begins a deep dive into Stark broadening. The

58

lengthy process in going from this starting point to a final expression of Stark broadening

profiles of the emission lines will not be presented in full here, and the reader is encouraged

to look at the incredibly thorough presentation in the aforementioned Griem textbook for

the mathematical details.

As mentioned above, the microfield distribution employed in this approach is given in

terms of the normal Holtsmark field strength F0, which is essentially the Coulomb field

strength produced by a perturber located one mean ion-ion separation length rp away from

the emitter [66]. This distance is defined as:

(cid:32)

rp ≡

3
4π

1
np

and so the normal Holtsmark field strength is:

(cid:32)

(cid:33)2/3

4
15

F0 = 2π

(cid:33)1/3

,

Zpe
4π
0

2/3
n
p

,

(2.9)

(2.10)

and the microfield distribution is given by the normalized Holtsmark distribution HR(β)

with β being the electric microfield strength F normalized to the normal Holtsmark field

strength F0, so:

β =

F
F0

.

(2.11)

In these equations, Zp and np are the perturber charge and density respectively, and e the

elementary unit of charge. This Holtsmark distribution is obtained by assuming all particles

to be statistically independent. Further details and derivations pertaining to this distribution

59

Figure 2.20: Reproduction of figure published in Ref. [8], illustrating changes to the mi-
crofield distribution with deviations from the Holtsmark distribution (R = 0), 
 is in units of

0. Symbols are different than those used in the thesis: the Debye shielding parameter sym-
bol is a, the field strength is 
, the normal Holtsmark field strength is 
0, and the normalized
distribution function is P (
).

are found in Ref. [66], but the result for the normalized Holtsmark distribution is:

(cid:90) ∞

0

HR=0(β) = H0β

xsin(βx)exp(−x3/2)dx , H0 = 2/π .

(2.12)

The last detail to mention regarding the background on the Stark profile is that the above

description is applicable for situations where the parameter R is close to 0. This, called the

Debye shielding parameter, is the ratio of the mean ion-ion separation to the Debye radius,

expressed as:

(cid:32)

R =

(cid:33)1/6

.

9e6ne

16π2(
0kTe)3

60

(2.13)

To get an idea of its value in a plasma typical of the PW, take ne = 1016 cm-3 and Te = 1.5
eV, which results in R ≈ 0.3. In the work for this thesis, the simplification of R = 0 was

taken, however, one could employ more accurate corrections, for example those described

and calculated in Refs. [8] and [70]. In Fig. 2.20, a reproduction of a figure published in

Ref. [8], it can be seen how the microfield distribution is adjusted from being the formerly

described Holtsmark distribution for R = 0 to different forms as R increases. In this figure,

the Debye shielding parameter symbol is a, the field strength is 
, the normal Holtsmark

field strength is 
0, and the normalized distribution function is P (
).

With the details of the electric microfield established, we can now move to the general

Stark profile shape. The profile is influenced by both electron-emitter interactions as well

as ion-emitter interactions. The electron-emitter interactions require what is called the

impact approximation, a view which is characterized by the collisions that occur rapidly

compared to the duration the atom radiates. These collisions are governed by linear Stark

effect perturbations to upper and lower wavefunctions of the emissions which gives rise to

a symmetric and shifted Lorentzian-shaped profile.

In contrast, ion-emitter interactions

require what is called the quasi-static approximation, which assumes that the perturbation

imposed by the colliding particle is nearly constant over the entire duration that the atom is

radiating. These collisions have a component of quadratic Stark effect perturbation, which

results in asymmetry as well as additional broadening introduced to the profile [7,64,66]. The

reason the quadratic Stark effect perturbations result in asymmetric broadening while linear

Star effect perturbations result in symmetric broadening is that the Stark shift resulting

from any given collision is given by:

δλif (F ) = Cif F n ,

(2.14)

61

where if denotes the initial and final states, F the perturbing field strength (recall the

Holtsmark distribution of this field), Cif being a constant associated with the transition,

and n = 1 and n = 2 being the case for linear and quadratic Stark effects respectively.

Broadening then is a result of many of these occurring over the aforementioned distribution

of the perturbing fields [66].

Ultimately, the Stark broadening profile is parameterized with the electron-broadening

parameter wj, profile shift d, and asymmetric ion contribution α. The Stark broadening

profile j(λ) for an emission of unshifted wavelength λ0 is given by:

(cid:90) ∞

j(λ) = jA

0

1 + [

HR(β)
2(λ−λ0−d)

wj

dβ ,

− αβ2]2

(2.15)

What is measured by the spectrometer is a convolution of the instrumental profile (IP)

and the Stark profile in Eq. (2.15), so:

(I ∗ j)(λ) =

(cid:90) ∞
−∞ I(t)j(λ − t)dt .

(2.16)

Here, the IP is given by I(λ), which is simply recast in the equation in terms of a dummy

variable t. The nature of the IP of the spectrometer used in this work is discussed below.

Once the IP has been ascertained, a least-squares minimization fitting routine is performed to

obtain the following parameters from Eq. (2.15) as a part of Eq. (2.16): electron broadening

width wJ , asymmetry parameter α, profile center (λ0 +d) (note, the Stark shift d itself is not

determined here), and profile amplitude jA. In reality, this can be simplified by imposing

a constraint on the width wJ and asymmetry parameter α such that they both provide the

same electron density ne, because both of these parameters scale with ne. These scalings

62

are given by:

and

wJ ∝ ne ,

α ∝ F 2
0
wJ

∝ n

1/3
e

.

(2.17)

(2.18)

As a result, one can use calculations of wJ and α at specified plasma conditions, as listed in

Appendix IV of Ref. [66], to couple the two parameters together, reducing the total number

of parameters that must be fitted by one.

Finally, the instrumental profile used in this work will be described in more detail. As

mentioned above, the fitting routine used to extract the Stark width (and therefore electron

density ne) critically relies upon knowing the instrument’s own line profile since the overall

observed profile is a convolution of the instrumental profile and the Stark profile, as in Eq.

(2.16). This profile arises as a result of the intrinsic characteristics of the internal optics and

collection components of the spectrometer such as entry and exit slits, gratings, or detector

properties [71]. Zonal aberrations in the optics can contribute to this, as could optical

misalignments, or some source of nonuniform angular intensity distribution of light entering

the spectrometer [72]. This is due to the fact that the light enters the spectrometer with

some angular spread, and so the aberrations, misalignments, and other physical imperfections

can produce a net effect of slightly different optical pathways for a particular wavelength.

The result of this is a perceived spread of the light of that wavelength, which we call the

instrumental profile [71–73]. A nice description of all the spectrometer components and how

they impact the ultimately observed spectrum can be found in Ref. [7].

63

Frequently, IPs are reasonably assumed to be Gaussian [64, 71]. However, this is not

always appropriate [71–73], and it is indeed inadequate in describing the shape of the Ocean

Optics HR4000 instrumental profile which is wavelength-dependent and appears to defy any

convenient analytical form. One possibility that could be further explored though is that the

spectrometer’s IP through at least some part of its wavelength range obeys a skew-normal

distribution, which Ref. [71] mentions is sometimes appropriate. This was not done in this

work. Instead, to ascertain what this shape truly is, low pressure gas discharge lamps of He

and Ar gas were used, which produce linewidths much narrower than the instrumental profile

width observed, indicating the results are broadened purely as a result of the instrumental

effects. The result of this is shown in Fig. 2.21, which shows the collected emission profile

at three wavelengths across the spectrometer’s wavelength range. For each line whose Stark

width is to be experimentally determined, an instrumental peak must be measured at that

wavelength (this makes the low pressure gas lamps a greatly convenient choice), and the

profile determined by applying a cubic spline to the measured peak points. Ref. [74] suggests

that the spectral width of detector pixels should ideally be about 10-20% of the FWHM of

the instrumental profile, but in the case of the Ocean Optics HR4000 instrument available

for the PW studies, this can be seen in 2.21 to be a far less ideal 30-40% of the FWHM.

This means that the points defining a peak are quite sparse, and the application of the

cubic spline to determine the IP doesn’t fully capture its shape. Utilizing a spectrometer

that had a longer focal length and/or the option of the user switching diffraction gratings

(greater groove density means narrower wavelength range but superior resolution) would

likely have afforded greater calculation reliability to this study. In Ref. [64], it is suggested

that ideally the instrumental broadening is at most 1/10 of the full width of the observed

profile, a condition which is not the case for the present work, especially in argon where the

64

Figure 2.21:
project. These profiles were acquired using a low pressure He gas discharge lamp.

Instrumental profiles for the Ocean Optics HR4000 spectrometer used in this

instrumental broadening can be up to about half the total measured width.

It should be noted that in the helium arc, some emissions are observed to have nearby

forbidden components which arise at higher electron densities [75, 76]. These are emissions

close in energy to allowed transitions, and can manifest where perturbing electric microfields

from high electron densities results in mixing of wave functions that ordinarily are disallowed

through usual dipole selection rules [66, 75]. This ordinarily forbidden transition is induced

at the expense of the allowed transition, and at the electron densities in the PW, is generally

about 20% the irradiance of the latter, but for much higher electron densities, can be of

65

389.00389.25389.50389.75471.50471.75472.00472.25501.75502.00502.25502.50502.75050100150200irradiance [a.u.]Wavelength [nm]roughly equal and even greater amplitude than the allowed transition at densities between

1017 - 1018 [77, 78]. The presence of such forbidden components is observed in the PW
spectra collected for a couple lines: the 447.15 nm line (1s2p 3P 0 − 1s4d 3D) has a forbidden
component lying at 447.0 nm (1s2p 3P 0 − 1s4f 3F 0), and the 492.19 nm line (1s2p 1P 0 −
1s4d 1D) has a forbidden component lying at 491.9 nm (1s2p 1P 0 − 1s4f 1F ). For both of

these localities, the upper states are coupled through the perturbing electric field via the

Stark effect [77] which is produced by charged neighbors in the vicinity of the emitting

particle. As a result, the compared characteristics of the allowed and forbidden components

of the emission provide another probe of the electron density. The behavior of these emission

components with plasma conditions have previously been thoroughly examined e.g.

in the

works of Refs. [75–80].

The authors of Ref. [77] provide an empirical formula for the relationship between the

He 447.15 nm allowed-forbidden separation s and the plasma’s electron density ne and

temperature Te. However they suggest this empirical relation is applicable for electron

densities between 5x1016 to 7x1017 cm-3, which is well above typical PW electron density.

This expression is given as:

log10(ne) = 21.5 + log10

(cid:33)b(Te)

(cid:35)

− 1

(cid:34)(cid:32)

s
s0

,

with

,

b(Te) = 1.46 +

8380
T 1.2
e

66

(2.19)

(2.20)

Figure 2.22: Sample Stark fits for the Ar I 425.9 nm and He I 447.1 nm emissions respectively,
for a representative operating condition of 200 torr (150 torr for He) and 150 A in a 6x6mm
PW, collected at P6/6. Instrumental profiles obtained by low pressure lamp discharge are
also shown. A forbidden component on the blue wing of the primary He peak is also seen
(this is not fitted).

67

425.6425.8426.0426.2426.405101520446.6446.8447.0447.2447.4447.6447.80510152025 Arc Emission Stark Fit Lamp EmissionIrradiance [a.u.]Wavelength [nm]Ar I 425.9 nmP6/6 of 6x6mm PW200 torr, 150 AHe I 447.1 nmP6/6 of 6x6mm PW150 torr, 150 AWavelength [nm]in which electron temperature Te is in K, s and s0 are in nm, and ne is in m-3. The value

of s0 is given as 0.1479 nm.

One potential improvement in the Stark profile fitting routine, particularly for those He

lines with forbidden components, would be to fit the entire profile to a calculated one, rather

than fitting the approximate parameterized profile in Eq. (2.15). Ref. [75], and more recently

Ref. [76] for example have calculated profiles for the He 447.15 nm line at a variety of plasma

conditions, and in fact also include the 447.0 nm forbidden component characteristics, which

is not fitted in the routine described and utilized in this thesis.

In Fig. 2.22, the Stark

broadening and forbidden component features described in the previous several paragraphs

are illustrated, along with Stark fits performed using the routine described above.

It is therefore important to get an idea of how close the electron density obtained from

Stark profile fits are to the average electron density over the cross sectional area at some

given axial location. Diagnostic plates available in this project provide a line of sight only

across the central chord of the channel’s cross section, and as a result an Abel transformation

to obtain radial distribution of the electron density is not possible. Having optical access to

off-center chords as well would enable one to more reliably determine the radial behavior of

emission irradiances and electron densities. Not having those measurements made here, we

will look to previous measurements and the PLASIMO model for a prediction of the shape

of the electron density profile. Results published by Timmermans et al in [81] in an argon

cascaded arc illustrate determined electron density radial profiles as seen from an end-on

view.

68

2.2.3 Electron Temperature

Another key property of a plasma that can be used characterizes its behavior is the electron

temperature, given by Te which plays a prominent role in the rates of interactions within a

plasma. As mentioned in Chapter 1, the EEDF is often assumed to be Maxwellian and given

by Eq. (1.14), a claim which will be quantitatively examined in Section 3.1. As a result, as

first mentioned in Section 1.2, for a given binary electron-impact reaction the rate constant

can then be obtained by:

K(T ) =

(cid:33)1/2(cid:32)

(cid:32)

1
πµ

2
kTe

(cid:33)3/2(cid:90) ∞

0

E σ(E) exp−E/kTedE ,

(2.21)

in which σ(E) is the process cross section as a function of energy, Te is the electron temper-

ature, and µ is the reduced mass (for electron-heavy collisions, this is essentially the electron

mass me).

The observed intensity of a given emission line is given by:

I =

Sa

4πr2 nuAul∆E , ∆E = Eu − El = hc/λ ,

(2.22)

where subscripts u and l refer to the upper (or emitting) state and lower state respectively

[47,82]. Note that all fine-structure states are grouped together into one, for the purposes of

this work. Additionally, Sa is light acceptance area at a location r away from the emitters

(and assuming an isotropic emission), nu is the emitter density, and ∆E is the emitted

photon energy and the energy difference between upper and lower levels. Lastly, A is the

spontaneous emission rate, which is obtained through a quantum electrodynamics treatment

of the emission [45], namely for a transition from sublevel mu of the upper level u to all

69

possible ml sublevels of the lower level l:

Aul =

8πe2∆E
3
0h2c3

(cid:12)(cid:12)(cid:12)(cid:104)1ml|(cid:126)r |2mu(cid:105)(cid:12)(cid:12)(cid:12)2
(cid:88)

ml

.

(2.23)

Note that in Eq. (2.22), every factor is either a property of the emission or the light collection

system, with the only exception being nu which is a property of the plasma within. Therefore,

establishing a connection between the plasma’s properties and the resulting excited state

population distribution for the collection of possible excited states means that one can use

the corresponding collection of emission irradiances to probe those same plasma properties

[7, 46, 47]. When electron-impact collision rates dominate over radiative rates, then the

relative populations of excited states assumes a Boltzmann distribution such that for states

1 and 2:

(cid:32)

exp

(cid:33)

,

−E2 − E1

kTe

n2
n1

=

g2
g1

(2.24)

where g is the state degeneracy, E the state energy, and Te is the electron temperature,

reflecting the fact that the levels assume their densities via electron-impacts [7]. If it is the

case that radiative processes are insignificant compared to collisional processes for all excited

states, the system can be said to be in local thermodynamic equilibrium (LTE), and this

condition generally requires a rather high electron density, greater than the value obtained

in the PW in this work. However, even at electron densities lower than the LTE limit, the

highly excited states may still meet the requirement of collisional processes dominating over

radiative processes and therefore Eq. (2.24) can still hold for these highly excited levels,

a conditions which is called partial local thermodynamic equilibrium (PLTE). This is not

always the case, and the conditions under which two given states obey Eq. (2.24) is discussed

70

in more detail in Section 2.2.3.1. If the plasma conditions do not meet the requirements for

at lease PLTE for the emissions being observed, it is still possible for the emission states to

obey a Boltzmann distribution and therefore Eq. (2.24) would hold as long as Te is replaced

by a generic excitation temperature Texc [44].

The spectral irradiances of the emissions are captured by the spectrometer discussed in

Section 2.1.3.1, but the emission’s overall irradiance is smeared over some wavelength range

due to the broadening mechanisms mentioned in Section 2.2.2. Spectral irradiances are

irradiances per unit wavelength, whereas the overall emission irradiance (what can properly

just be called irradiance) is integrated over the peak’s wavelength or frequency extent. In

Chapter 4 of Ref. [7], the author provides a rather comprehensive discussion of these and more

often confusing terms pertaining to light fluxes and their detection. As a result, from here

on out when emission irradiances are mentioned, it is the value obtained by integrating over

the line profile. Furthermore, Eq. (2.22) would be correct for the case in which the emitted

photons do not suffer from any reabsorptions elsewhere in the plasma prior to detection.

If this condition is met for a given transition, it is said to be optically thin. The case of

optically thick lines is treated in Section 2.2.4, but we will assume that the only lines which

sustain any appreciable reabsorption will be resonance lines which decay to ground state.

Combining Eq.

(2.22) and the state density scaling in Eq.

(2.24), and maintaining the

general form in which Te is replaced by Texc, the emission properties can be rearranged as:

(cid:32)

(cid:33)

This expression can be applied to multiple emission lines and X-Y points where X = Eu

and Y = ln

IA
gu

. Note that the geometric factor Sa

4πr2 would be just an additive constant

71

(cid:33)

(cid:32)

ln

IA
gu

= − Eu
kTexc

.

(2.25)

Table 2.3: Selected Ar II emission properties for lines studied in this work.

λ [nm]

Emitting state

Eu [eV]

gu

A [s-1]

Accuracy

[Config., Term, J]
3p4.(3P).4p 2So 1/2
3p4.(1D).4p 2Fo 5/2
3p4.(1D).4p 2Fo 7/2
3p4.(3P).4p 4Po 3/2
3p4.(3P).4p 4Po 5/2
3p4.(3P).4p 2Do 5/2
3p4.(3P).4p 4Po 5/2

457.93

458.99

460.96

473.59

480.60

487.99

500.93

19.973

21.127

21.143

19.261

19.223

19.680

19.223

2

6

8

4

6

6

6

8.00x107
6.64x107
7.89x107
5.80x107
7.80x107
8.23x107
1.51x107

<10%

<3%

<3%

<3%

<3%

<3%

<10%

Table 2.4: Selected He I emission properties for lines studied in this work.

λ [nm]

Emitting state

Eu [eV]

gu

A [s-1]

Accuracy

[Config., Term, J]

1s5d 1D 2
1s4d 1D 2
1s3p 1Po 1
1s4s 3S 1

1s5d 3D 3,2,1
1s4d 3D 3,2,1

438.79

492.19

501.57

471.32

402.62

447.15

24.043

23.736

23.087

23.594

24.043

23.736

5

5

3

9

26

26

8.9889x106
1.9863x107
1.3372x107
3.1736x106
6.6926x106
1.3882x107

<0.3%

<0.3%

<0.3%

<0.3%

<0.3%

<0.3%

to this expression, but has been dropped from this equation due to it simply being an offset

value. From this, performing a simple linear fit allows one to use the slope to determine

Texc. This is the commonly employed Boltzmann line method [46, 47, 82].

The emission properties listed in Tables 2.3 and 2.4 are obtained through the NIST

database [83], and further information on the notation used for the excited electronic states

can be found in Ref. [84].

In the wavelength range of the Ocean Optics HR4000 spectrometer used (about 385 to 515

nm), the observed Ar I emissions do not span a wide range of upper state energies, making

the Boltzmann line method unreliable for these emissions, however Ar II lines are plentiful,

intense relative to background, and have a relatively large span of emitting state energies

72

so these are used for determining Texc in argon arcs in this work. Ultimately, Ar II lines

appear to be adequate for determining electron temperature, but this is not true for observed

emissions helium. This will be explained in Section 2.2.3.1. This would confirm the suspicion

that the Texc obtained via Boltzmann plot for helium emissions is not representative of the

actual electron temperature Te because it is far lower, around 0.3 to 0.6 ev, than would

be expected necessary to maintain ionization to sustain the arc. It is therefore required to

have another means of backing out what the electron temperature Te is from relative He I

emission irradiances. As a result, we will need to explore an additional tool to back out an

electron temperature resulting in the observed relative He I emissions. This tool is called a

collisional-radiative (CR) model, and will be explored in Section 3.2.

2.2.3.1 Applicability of Partial Local Thermodynamic Equilibrium

In partial local thermodynamic equilibrium (PLTE), high-lying excited states of an atom

or ion are in thermal equilibrium with electrons, and follow Saha-Boltzmann distributions

[44, 52, 85],. The significance of this is that the excitation temperature which defines the

distribution of the excited states, Texc is equivalent to the electron temperature Te. Many

different theoretical approaches to determining the conditions under which PLTE is applica-

ble, which are briefly summarized in [85]. All are predicated on the condition that above a

certain level threshold, electron-impact rates for a given transition should exceed the corre-

sponding radiative rates by at least an order of magnitude [52, 85]. Level populations nk of

levels above the threshold are related to the next ion stage ground-state population ni via

73

the Saha-Boltzmann relation [52, 85]:

neni
nk

=

2gi
gk

(2πmekTe)3/2

h3

(cid:32)

exp

(cid:33)

.

−(Eion − Ek)

kTe

(2.26)

In this expression, gi is the degeneracy of the ground state of the ion, gk is the degeneracy

of the excited state k, Eion is the ionization energy (relative to the ground state), Ek is the

energy of level k, and electron mass, density, and temperature are given by me, ne, and Te

respectively.

When this equation is satisfied, the levels are said to be in Saha excitation equilibrium.

The task then is to determine what the threshold level is, above which Eq. (2.26) is valid,

and therefore a Boltzmann plot of emissions originating higher than the threshold provides

an excitation temperature such that Texc = Te. The descriptions of various workers’ criteria

for this PLTE threshold are frequently somewhat ambiguous, particularly for non-hydrogenic

systems atomic excitation and ionic excitation distributions, a category into which the PW

studies in both helium and argon fall, although it is sometimes assumed, particularly for

light elements, that highly excited states are close enough to hydrogenic that derived criteria

can still apply to them [50, 86, 87]. We will start by examining the criterion established by

Griem [50, 52]. This criterion, in terms of an equivalent excited principal quantum number

ncr (note this n represents a quantum number, not a number density such as ne) is given

by:

(cid:33)3(cid:35)2/17(cid:32)

(cid:34)

(cid:32)

αf
a0

5
π

z7
ne

kTe
z2EH

(cid:33)1/17

.

ncr ≈

(2.27)

With this, for excitations originating from a state exceeds this critical principal quantum

number ncr. In this, a0 is the Bohr radius (if in units of cm then the electron density will be

74

in units of cm-3), αf is the fine structure constant, EH is the ionization energy of hydrogen,

and z represents the ionization stage (z = 1 for neutral excited states, z = 2 for singly-

ionized excited states, etc.). This can be rearranged to obtain instead a critical electron

density ne,c1 for emission lines of known quantum number n:

(cid:34)

(cid:32)

(cid:33)3(cid:35)(cid:115)

nec1 ≥

5
π

z7

n17/2

αf
a0

kTe
z2EH

.

(2.28)

Griem mentions this criterion is properly applicable only to hydrogenic systems [50],

however also mentions that it should also be relatively appropriate for higher excited levels

of light atoms or ions. Despite it often being applied to Ar I and Ar II plasmas, it’s not clear

if the upper levels of Ar I and Ar II do obey a hydrogenic energy scheme and therefore it is

unclear if this is appropriate in these plasmas [82, 88].

A second criterion is derived in Ref. [44] and is utilized in Ref. [88], which is approxi-

mately:

(cid:32)

(cid:112)

Te

nec2

EH
∆Ei

(cid:33)9/2

z ≥ 8 × 1017 .

(2.29)

The critical electron density evaluated with this criterion, nec2 is in units of cm-3. The ∆Ei

is the ionization energy of the state in question. In this, Te is given in eV. Rearranging, Eq.

(2.29) gives the criterion in terms of electron density:

(cid:32)

(cid:33)9/2

.

(2.30)

nec2 ≥ 8 × 1017

√
1
Te

z

∆Ei
EH

The third criterion that will be mentioned here is that in Ref. [87]. This third criterion,

75

Table 2.5: PLTE criteria for He I and Ar II emissions. Argon Te is 1.5 eV and the Ar II
level under consideration is 4p 4Po 5/2. For Helium Te is 2.0 eV and He I level is 3p 1Po.

Criterion Ar II critical ne [cm-3] He I critical ne [cm-3]

1

2

3

6.8 × 1014
9.9 × 1015
7.1 × 1015

1.4 × 1014
2.8 × 1013
4.9 × 1016

with the electron density again in units of cm-3, is given by:

nec3 ≥ 1.15 × 108z

(cid:112)

kTe

gj
gi

(Ej − Ei)

E

3/2
H

(cid:80)

h<j Ajh
fij

(cid:33)

(cid:32)

Φ1,2

Ej − Ei
kTe

.

(2.31)

In this, states j (upper) and i (lower) originate from adjacent levels whose energies and

degeneracies are given by E and g respectively, and EH is the ionization energy of hydrogen.

Note that for this, energies and kTe should be in the same units. Also included in this

equation is the summed rates of all other transitions originating from the upper state j,

(cid:80)

(cid:33)

(cid:32)

Ej−Ei
kTe

h<j Ajh and the oscillator strength between the adjacent levels fij. Finally there is also

a factor Φ1,2

which is tabulated in Ref. [87], which are factors associated with

electron-impact excitations.

Some estimates of these critical electron densities from all three references are presented

in Table 2.5, for both helium and argon. The electron temperatures of 1.5 and 2.0 eV for

argon and helium respectively and the Ar II and He I levels used as a test case has one

of the lowest emitter state energies in the wavelength range observed for Ar II and He I

respectively. These states are given in the caption of Table 2.5. A sizeable amount of spread

exists between the critical electron densities given by the methods, in all three cases for Ar
II, the measured electron densities which in the argon PW generally exceed 1 × 1016 [cm-3]

are sufficient to achieve PLTE for the emitting states in our observation range. For the case

of helium, the conclusion is less obvious, as the measured electron density is typical around

76

2 × 1015 [cm-3], which results of the first two criteria suggest allows PLTE, but the third

criteria does not. Given this uncertainty for He I emissions, we will not assume the existence
of PLTE for these emitting states and therefore that the He I Texc (cid:54)= Te. However, for the

Ar II emissions, we will assume the existence of PLTE for the observed emitting states and

therefore that Ar II Texc = Te.

2.2.4 Radiation Reabsorption

Radiation emitted through the process of de-excitation can be reabsorbed at a different lo-

cation within the plasma via the inverse process. Taking a packet of photons whose initial

intensity is I(λ), impinging on a layer of absorbing particles (these would be those par-

ticles in the lower excited state corresponding to the emission whose reabsorption we are

investigating), ds thick. The loss of intensity of that original packet of photons is:

dI(λ) = −I(λ)σabs(λ)nl ds ,

(2.32)

where σabs is the photon absorption cross section and nl is the absorbing state density.

Integrating this over an absorbing distance D:

I(λ) = exp(−σabsnlD) .

(2.33)

The quantity inside the exponent on the right hand side is often grouped into the unitless

parameter τ (λ), called the spectral optical depth of the plasma at wavelength λ [45, 89, 90],

so:

τ (λ) = σabsnlD

77

(2.34)

,

with the photon absorption cross section is given by:

σabs =

λ4
0
4πc

gu
gl

A f (λ)

(2.35)

.

In this, the emission’s central wavelength is given by λ0, c is the speed of light, gu and

gl are the upper and lower state degeneracies respectively, A is the Einstein spontaneous

emission rate, and f (λ) is the absorption profile (we will assume this to be of the same

shape as the emission profile). As noted previously, Stark broadening is the dominant source

of non-instrumental broadening (the absorption occurs entirely within the plasma, so the

instrumental profile plays no role here) for the Ar I and He I lines in this work. However, it

should be pointed out that Ar II emission lines have significantly narrower Stark broadening,

such that it is on the order of the Doppler broadening degree. For simplicity though, we will

still assume that we can just look at the Stark profile in Eq. (2.15) and even further simplify

matters by ignoring the ion-broadening contribution, giving us an emitting/absorbing profile

that is purely Lorentzian. This vastly simplifies the analysis and lets us write a relatively

compact expression for the absorption profile:

f (λ) =

wj

j + (λ − λ0 − d)2
w2

.

(2.36)

As before, wj is the Stark width and d is the Stark shift for the particular emission line in

question, at the plasma electron density. With this one can determine the spectral optical

depth across the emission profile, τ (λ). Resonant emissions which decay to the ground state

will have have a much larger absorbing density nl as well as a much greater absorption cross

78

section σabs due to the lines being much narrower than emissions which correspond to decays

to still-excited states, these are the lines which will suffer the must reabsorption by far [66].

If the plasma is both absorbing and emitting (this is the case for the PW), this optical

depth can be used to calculate what is called an escape factor g(τ (λ)), essentially the fraction

of the total emitted light over the distance which ultimately escapes the plasma. An escape

factor of 1 means there is negligible absorption and the line is said to be optically thin. The

spectral escape factor is given by [90]:

(cid:16)

g

τ (λ)

(cid:17)

= 1 −

(cid:33)3(cid:34)

(cid:32)

λ0
λ

(cid:16) − τ (λ)

1 − exp

(cid:17)(cid:35)

,

(2.37)

though what is more often reported is the overall escape factor, obtained by averaging over

the profile so that:

(cid:33)3(cid:34)

(cid:90) (cid:32)

λ0
λ

(cid:17)(cid:35)
(cid:16) − τ (λ)

1 − exp

g(τ ) = 1 −

f (λ)dλ .

(2.38)

Some implicit assumptions that are fairly reasonable in this are that stimulated emission has

been ignored, and the absorbing and emitting profiles are identical in shape, which effectively

means the plasma is uniform [90].

2.3 Cathode Longevity

As mentioned in Section 1.1, the application of the plasma window as a charge stripper

for an ion accelerator facility naturally demands that the plasma window be capable of

operation continuously for the duration of a typical experiment which utilizes the accelerator

facility. For example, at the NSCL where experiments are conducted on nuclear properties of

79

primarily rare isotopes, the duration is maximally about two weeks, as mentioned in Section

1.1. There are a great many cathode-specific variables which can impact their operating

lifetime, especially in the case of using tungsten doped with impurities that lower the work

function (WF). Due to attention in the PW project being concentrated on plasma phenomena

and long-term arc stability challenges, empirical data on cathode lifetime is very limited for

the PW study at this point. Here an effort is made instead to survey relevant literature and

compile conclusions, so that suggestions for PW cathode improvements can be made. Some

studies seem to suggest that, although the PW studied in this thesis was unable to operate

continuously for nearly this length of time, cathode operation in arcs of up to 1000 hours

is possible.

In Ref. [91], using an argon cascaded arc very similar to our own, operating

around 50 A and a half-atmosphere, it is claimed that their thoriated tungsten cathodes

typically operated for about 500 hours before replacement was needed.

In Ref. [12], the

authors operated their thoriated tungsten cathodes in a 60 A arc at 600 torr beyond 1000

hours.

Although dimensions may vary from study to study, all references in this section which

investigated cathode performance in various conditions used cone-tipped-rod cathodes, the

same geometry type used for the plasma window.

It is well known that for an electron

to escape from the cathode and participate in electric current to the anode, it must either

overcome the WF, or tunnel through the potential barrier. A great many materials are used

in a great many applications, but a survey of literature in this work will primarily be focused

on the performance of tungsten, WF = 4.6 eV, doped with thoria (ThO2), reduces WF to 2.8

eV or lanthana (La2O3), reduces WF to 3.0 eV [92], also referred to as thoriated tungsten

and lanthanated tungsten respectively. In the PW work, thoriated tungsten cathodes were

primarily used.

80

Figure 2.23: View of the NSCL PW cathode tips from inside the cathode housing, looking
down the channel towards the anode. Banding structure is visible on the used ThO2-W
cathodes, signifying regions of varying thorium concentrations, as described in Refs. [9–11].

Some features of the cathodes that are necessary for plasma window operation are a

sharp tip, so that the arc can be initialized via field emission (using a Tesla coil), even

though it subsequently maintains electron supply and current via thermionic emission, as

first mentioned in Section 2.1.2. In our system, the cathode housing has three channels into

which the cathode needles are inserted such that their tips are on a 4.5 mm diameter circle.

This can be seen in Fig. 2.23 which shows a view of used cathodes tips inside the housing,

looking down the channel towards the anode. The channel diameter in the cathode housing

is about 13 mm diameter, shown in Fig. 2.24. The channel diameter subsequently reduces

down to the PW channel size of 6 mm or 10 mm, depending on the aperture of the first

plate.

Broadly, the two phenomena impacting cathode lifetime are shape deformation and mor-

81

Figure 2.24: Cathode housing (without cathodes), view from the PW-side face. The housing
channel is 13 mm diameter, which then constricts down to 6 or 10 mm diameter, depending
on the aperture of the first PW plate.

82

phology changes [10, 12, 93]. Drawing conclusions regarding optimization of cathode char-

acteristics is challenging due to the interplay between numerous properties and phenomena

such as cathode geometry, cathode material, gas used, cooling, and current density [10, 94].

The emission-enhancing dopants mentioned earlier in this section provide a reduced WF on

the surface of the cathode, yet being in a matrix of tungsten provides shape stability due

to its high melting point. Without the presence of the WF-lowering dopant, the operating

temperature of the cathode is much higher, and the material removal rate is far greater.

This higher operating temperature manifests as a result of a greater cathode fall potential

being necessary to drive ion collisions of sufficiently high energy to exceed the large WF to

the electron emissions which sustain the arc. Evidence of this can be seen in Fig. 2.25. In

this, pure tungsten cathodes and thoriated tungsten cathodes were each tested for about

the same amount of operating time, about 30 minutes. The pure tungsten cathodes suffer

substantially greater shape deformation, having the neck reduced as well as the formation

of surface roughness. This illustrates the necessity of having a WF-lowering dopant in the

cathodes.

During cathode operation, there are two competing processes which effect the presence

of the WF lowering dopant (consider thorium) on the cathode surface: desorption or evapo-

ration of thorium atoms from the hot surface, and the supply via diffusion from the cathode

bulk [95]. In this cathode modeling study, it was concluded that there are primarily two

regimes of cathode operation. The first one is characterized by a lower operating tempera-

ture, and in this regime there is nearly a monolayer of thorium coverage over the cathode’s

emitting surface. Over time this thorium coverage degree decreases until reaching some

critical value, beyond which the surface temperature rapidly rises and the dopant cover-

age rapidly decreases to nearly zero, signaling the arrival of the second operation regime.

83

Figure 2.25: Top-Left: Thoriated tungsten cathodes after about 30 minutes of operation.
Bottom-Left: Pure tungsten cathodes after about 30 minutes of operation. Right: Zoom of
the pure tungsten cathodes, illustrating neck reduction and formation of surface roughness.

Now the operating temperature is much higher and cathode material will be more rapidly

depleted. In Ref. [95], this is identified as effectively the end of cathode operating lifetime.

There are some key findings in Ref. [95] that are worth mentioning. Firstly, the authors

determined that an often-overlooked contribution to the cathode’s internal temperature dis-

tribution is Joule heating from the current. Higher temperatures in the vicinity of the

emitting surface encourage thorium diffusion to it and therefore delay the aforementioned

rapid removal of surface thorium and rapid surface temperature increase, thus extending

the cathode lifetime. Therefore, while higher currents result in more rapid surface thorium

removal, that removal is compensated to a greater degree by the higher Joule heating. In

general, the authors present the conclusion that a shallower temperature gradient through

the cathode enables greater cathode lifetime, supporting the same conclusion obtained in

84

Ref. [93]. A cathode model of the sort established in this publication could be helpful in

guiding improved PW cathode designs.

In the modeling study of Ref. [93] it is emphasized that the potential lifetime of a rare

earth oxide doped tungsten can be extended by a favorable temperature distribution within.

The case investigated here was W-ThO2, and although chemical processes were neglected in

this study, the author found that the balance between adsorption of dopants from the cathode

surface, and diffusion-replenishment of those dopants from the cathode bulk to the surface

were key in establishing the cathode’s service lifetime. Additionally, the author concluded

that longer electrodes, owing to a less steep temperature gradient, allow for greater diffusion

and therefore extend the cathode lifetime. Diffusion in shorter electrodes can only occur over

a shorter length. The authors furthermore posit that a thinned diameter, or neck, along a

cylindrical cathode can potentially increase the lifetime by acting to increase thermal and

diffusive resistance, though it’s suggested experimental investigation is needed to provide

evidence one way or the other. Similar to what was described in Ref. [95], Nemchinsky

posits that there are distinct stages in the lifetime of a refractory metal cathode doped with

a rare earth oxide (thoria in this case). An initial stage in which intense diffusion results

in a thick layer of thorium, though diffusion is overtaken by evaporation from the surface

at some point, and eventually only a monolayer of the thorium remains on the surface.

This process precedes the two stages focused on in Ref. [95]. In the second stage, parts of

this monolayer are evaporated so that the overall coverage ratio is less than unity, causing

the work function and surface temperature to increase. This then results in accelerated

evaporation and diffusion.

In a separate modeling study, in Ref. [96], the same author studied the effects of gas

swirl on the rate of erosion of cathodes, although this was studied for a hafnium cathode

85

operated in an oxygen plasma gas. In this it was shown that erosion rate is significantly

enhanced with greater gas swirl in the vicinity of the cathode. The posited rationale is that

the inclusion of swirl enhances the flow at the cathode and effectively acts to sweep away

ions from the cathode region. It is unclear what the implications are for arc stability from

the degree of swirl in the cathode vicinity, though it may suffer as well. This has relevance

to the PW setup because of the several channel size changes in the vicinity of the cathode:

entrance of cathode housing is 10 mm diameter, then it opens to 13 mm where the cathodes

are inserted to the channel (see Fig. 2.24), then constricts down to the 6 or 10 mm diameter

of the first PW plate.

One negative attribute of thoriated tungsten cathodes was investigated in Ref. [11] in

which it is suggested that while thoria-activated tungsten electrodes are useful regarding

the ease with which the arc can be initiated using them, they are prone to instability. The

study investigated investigated cathodes of a number of different rare earth oxide dopants

in tungsten, found lanthana-activated electrodes to overall sustain longer lifetimes. The

W-La2O3 electrodes were shown to have the lowest work function and therefore the lowest

operating temperature. During operation, the local quantity of oxides tends to decrease,

and large tungsten crystals form at the tip of the W-ThO2, as opposed to the W-La2O3

which was somewhat more resilient to this effect, and so had more consistent operation

with time. For this reason, the authors found that La2O3 can more easily migrate through

the cathode bulk to the surface to replace the emitting material that is vaporized during

operation. The arc discharges were around 200 A for up to 1 hour of continuous operation.

Electrode geometry in this study was similar to that in the present PW work, a cylindrical

base (1.6 to 3.2 mm diameter) with a conical tip.

Conversely, one feature that negatively impacts the appeal of W-La2O3 was investigated

86

by Ref. [97], which is so-called flickering of the arc, caused by fluctuations of the cathode

attachment point. The authors of this study find that W-La2O3 electrodes suffer a greater

flickering effect than do W-ThO2 electrodes. The flickering is attributed to the much lower

adsorption energy of La (5.6 eV) than Th (7.4 eV) which may result in more rapid surface

impurity depletion, in addition to the higher vapor pressure of La than Th resulting a lower

thermal stability of the surface.

Flickering has also been observed in the plasma window, likely attributable to the same

phenomena.

In some cases, it is sufficient to cause the arc to collapse and a cessation

of current flow, which in the plasma window has almost always occurred during helium

operation rather than argon. We refer to this occurrence as the arc collapsing, and it is

not surprisingly a highly undesirable occurrence and any measure that can be employed to

reduce its likelihood should be explored.

In Ref. [98], some properties of W-ThO2 and W-La2O3 cathodes were examined in both

pure argon gas and in argon with oxygen impurity gas. They concluded that the the pres-

ence of oxygen enables rapid oxidation of the cathode surface, which then first evaporates,

dissociates, and finally the tungsten is redeposited a ways from the hot tip, forming a rim at

a distance away from the tip which depended on cone angle and arc current. The authors

furthermore observed a constriction of the arc from the cathodes with the addition of 1%

oxygen to argon gas, causing a greater temperature at the attachment point. All in all, it is

concluded that the presence of oxygen impurity in the plasma reduces the usable lifetime of

the cathode, which only adds to the importance for the PW to be used with pure gas targets

in the context of gas charge stripping.

Authors of Ref. [12] discuss the impact of different dopant concentrations on cathode

performance, and are notably one of the exceptionally few studies to have observed behavior

87

after very long term operation, both after 400 and 1500 operation hours. In addition to the

crystallographic orientation of the emitting surface, the work function can be dramatically

influenced by the adsorption of atoms of higher electronegativity than the base material

(tungsten in this case). The authors provide an example of an oxygen layer on tungsten

increasing the work function by more than 1 eV, and an opposite effect for atoms of lower

electronegativity adsorbed such as thorium or lanthanum on tungsten. Existence of long-

duration emission requires low evaporation rate of the emission-enhancing oxide. These

authors noted that the cathode burn-back (length of cathode removed during operation)

over 400 hours of operation of W-La2O3 for their particular setup is around 0.4 mm, and

didn’t discern any clear trend with respect to the impurity concentration.

Also noted in this work is the fact that thorium’s low vapor pressure compared to other

explored elements including lanthanum, as shown in Fig. 2.26. This is a copy of a figure

in Ref. [12] that indicates that to achieve the same vapor pressure of metallic thorium, a

cathode with lanthanum needs to be 400 K less than the thorium one. However, although

thorium has a lower vapor pressure than lanthanum, it has a higher work function and

so higher temperature. The degree of this temperature difference is also mentioned in the

work of Ref. [10] to have a range of between 200 and 500 K depending on the size of grain

boundaries. This brings us to another key result of their work, that the larger the size of

grain boundaries, the lower the work function for thoriated tungsten cathodes, since the

farther from the boundaries the less thorium evaporates from the surface.

In Ref. [10], thoriated tungsten cathode surface features were examined after up to an

hour of operation with several parameters under investigation, including the plasma gas

composition (argon or helium), and the cathode geometry (pointed tip or flat tip). It was

found that for both cathode geometries, when operated in helium the cathode temperature

88

Figure 2.26: From data published in Ref. [12], this figure shows vapor pressures of metallic
thorium and lanthanum as a function of temperature.

89

120014001600180020002200240026002800300010-1110-1010-910-810-710-610-510-410-310-2Vapor Pressure [bar]Temperature [K] Lanthanum ThoriumFigure 2.27: Left: A photo of PW cathodes after operation in He gas, showing a series of
bands at different distances from the cathode tip. Right: a copy of a figure published in
Ref. [10] which investigated similar behavior for thoriated tungsten cathodes operating in
helium. Their surface morphology studies enabled identification of the bands as labeled.

was much greater than that in argon, resulting in rapid vaporization of cathode material

which then was ionized and redeposited back to the cathode as ionic current. The energy

released at the cathode surface by impinging ions determines the cathode temperature, and

is a function of the ionic current (suggested to be 15 to 50 % of the total current density),

the ionization energy, and the cathode fall potential drop. The overall effect is that when

operated in helium, the cathode surface temperature is much higher than in argon, and

approaches the boiling point of tungsten (5930 K). The redeposition occurs farther away

from the tip of the cathode, resulting in bands of different materials.

The authors found that, in argon after about 5 minutes of operation, the thoria in the

cathodes was mobilized and migrated towards the cathode surface, then moving laterally

and forming high-concentration thoria regions. As a result of this migration and the accom-

panying change in surface work function, during this period the total arc voltage drops from

90

29 V to 26 V. Although the authors concluded there was a significantly greater amount of

vaporization for the cathodes in helium, the net cathode mass loss was similar in both gases.

Given this complexity of material concentration banding of the cathodes evolving through

use, and doing so differently in argon or helium, it is likely that cathodes operated, for exam-

ple, in argon for some period of time prior to shifting to helium operation would have their

properties and operable lifetime adjusted from those if it were operated only in helium from

the start. Understanding of this potential phenomena could greatly benefit from additional

research. This is relevant to operation of the PW because it was necessary in our work to

initiate the arc in an argon flow first and then transition to a helium flow.

91

Chapter 3

Background and Models

The models presented in this section are included to lend support to measurements of certain

plasma properties as well as to enable calculation of others that are not measured.

3.1 Electron Energy Distribution Function

As with all collections of particles, there exists for the electrons in the PW a distribution of

their associated random kinetic energies, which is characterized by an electron temperature

Te. Fully equilibrated, the distribution function takes on a Maxwellian shape (this was also

briefly mentioned in Section 1.2), given by:

(cid:114)

f (E, T ) = 2

(cid:33)3/2

(cid:32)

1
T

(cid:32)

exp

(cid:33)

,

−E
T

(3.1)

E
π

This distribution is expressed such that the integral of the entire distribution, over all ener-

gies E, is equal to unity. The temperature T is identified as the electron temperature Te if the

EEDF is a Maxwellian shape, otherwise it is identified as an effective electron temperature

Tef f . However, there are instances where this form is inadequate for describing the electron

energy distribution function (EEDF), as mentioned in [99]. The reason this may occur in

plasmas is because electron-impact inelastic processes - excitations or ionizations of the heavy

particles - cause the impacting electron to lose kinetic energy by at least the corresponding

92

threshold energy. If the electron temperature Te, is such that these threshold energies lie

within the less-populated tail of the distribution, then rapid inelastic occurrences may result

in depletion of the high energy electrons in the distribution tail and hence elevated impor-

tance of elastic energy losses. The process of restoring the shape back towards Maxwellian

shape (sometimes called Maxwellization) occurs primarily through electron-electron colli-

sions. This section is devoted to examining rates of such inelastic processes and determining

if Eq. (3.1) is appropriate for describing the electron energy distribution function (EEDF),

or if the rapidity of inelastic collisions is sufficient to cause deformations in the EEDF tail.

In existing literature, thorough investigations of the appropriateness of a Maxwellian

EEDF for a plasma regime typical of the PW are very few. Generally it is simply taken

as an assumption that the EEDF in most achievable arc environments is Maxwellian, and

indeed in Ref. [50], Griem claims that in plasmas of at least moderate density and low
temperature (ne ≥ 1 × 1016 cm-3 and Te ≤ 5 eV), the EEDF is almost always Maxwellian.

This is attributed to electron-electron collisions being so frequent that they can overcome

any EEDF tail-depletion mechanisms, i.e.

ionization and excitation, especially from the

low-lying energy levels Ref. [87]. However, the actual collision frequency threshold criteria

for electron-electron collisions is not mentioned. In Ref. [87] it is also mentioned that super-

elastic electron collisions that force an excited state into a state of lower energy may also

play a role, however we’ll not examine these here. The conditions in the PW usually meet

the above density and temperature requirements, but in the interest of thoroughness, it’s

worth making a short excursion to quantitatively investigate the likelihood that our typical

arc plasma of the PW has a Maxwellian-shaped EEDF.

We do so by considering relative frequencies of two inelastic, tail-depleting processes:

excitations from the ground state to the lowest-lying excited state, and ionizations from the

93

ground state. These are then compared to the frequency of electron energy-transfer collisions

which push the EEDF back towards a Maxwellian shape. If the former are many orders of

magnitude less than the latter, we will assume that the EEDF does not stray far from a

Maxwellian shape. We consider the reactions from ground state and not those from the

metastable states for several reasons: firstly, we have a means of obtaining reactant density -

i.e. the neutral density nn - modeled via PLASIMO (discussed in detail in Section 3.5) which
is likely a decent approximation of the ground density ngrd in the PW, so ngrd ≈ nn. We do

not have a straightforward means of obtaining for example the metastable-state densities.

Our second reason, however, is that the inelastic processes such as ionization originating

from such metastable states have much lower threshold energies than the processes from the

ground state. As a result, the threshold energy where electrons can first start participating in

the reaction from a metastable state has substantially more electrons than at the threshold

energy for the process from the ground state. This is illustrated in Fig. 3.1 by comparing

the EEDF value at the ground-excited or ground-ion threshold energies given by the drop

lines (black for Ar and red for He) to the approximate threshold value for ionization from

metastable (the purple drop line, approximate for both gases). In this figure, the black solid

curve is the EEDF for a temperature typical of the Ar discharges in the PW and the red

dot-dashed line similarly for He discharges.

An energy-transfer collision frequency, as defined in Ref. [100], is the rate at which the

pre-collision kinetic energy of a projectile-target pairing changes divided by the pre-collision

kinetic energy. The velocity-dependent electron-electron collision frequency is given by [100]:

ν(v) = 8πne

e2
4π
0

lnΛ
m2
ev3

(3.2)

(cid:32)

(cid:33)2

94

Figure 3.1: Maxwellian EEDFs for two electron temperatures, one typical of Ar PW dis-
charges (black solid line) and one typical of He PW discharges (red dot-dashed line). For
that element’s corresponding line, drop lines are given for the lowest-lying excited state and
ionization energies, as well as at 4.5 eV (close to the value for ionization from the lowest
metastable level for both gases).

95

0510152025301E-81E-71E-61E-51E-40.0010.010.119.23E-24.5 eV7.10E-215.76 eV1.16E-411.55 eV1.39E-31.33E-419.82 eV1.51E-524.59 eVMaxwellian EEDF Value [1/eV]Electron Energy [eV] Te=1.6 eV Te=2.1 eVAveraged over a Maxwellian EEDF, the mean collision frequency is given by:

(cid:32)

(cid:33)2

νee =

√
ne
2π
3

e2
4π
0

4π(cid:112)meT 3

e

lnΛ .

(3.3)

In these, electron density, mass, velocity, and temperature are given by ne, me, v, and Te

respectively, and lnΛ is the Coulomb logarithm, which is the logarithm of the maximum to

minimum impact parameters for binary collisions of two charged particles. In a plasma, the

Debye shielding provides the value of maximal impact parameter and the minimal impact

parameter is the classical distance of closest approach [5]. This results in:

(cid:104)ζ(cid:105) =

2(m1m2)
(m1 + m2)2

σm
σsc

.

(3.4)

In this, σm is the momentum-scattering cross section and σsc is the full scattering cross

section. As a result, any such elastic collision between a heavy particle and an electron implies
that there is very little energy exchange, whereas for electron-electron collisions, (cid:104)ζ(cid:105) = 1/2.

This is the reason for the claim that electron-electron collisions are by far the most dominant

mechanism in restoring the EEDF shape and thus the reason we focus on this rather than

electron-heavy collisions as a means of Maxwellization [101]. Table 3.1 illustrates the relative

frequencies of interactions discussed in the preceding paragraphs under conditions typical

of the PW. In the first table, the identifiers OC1 and OC2 are shorthand for “operating

conditions set 1” and “operating conditions set 2” and their corresponding GCS pressure

and arc current values are indicated in the table. Note that all of these calculations are

performed based on measurements obtained at P2/6 of a 6x6mm PW.

To examine the effect of the inelastic processes on the EEDF, we start by assuming

that the initial EEDF is a Maxwellian shape, so that previously mentioned rate constant

96

Table 3.1: Plasma properties used to study Maxwellization of the EEDF.

Property [units]

Value for He OC1

” for He OC2

” for Ar OC1

” for Ar OC2

GCS Pressure [torr]

Arc Current [A]

Electron Density [cm-3]

Electron Temperature [eV]

Neutral Density [cm-3]
Electric Field [V/m]

e-e energy transfer

collision frequency [s-1]

150

105

1.8 × 1015

1.9

1.2 × 1017

1270

9.3 × 109

150

150

2.3 × 1015

2.0

1.1 × 1017

1300

1.0 × 1010

200

60

1.2 × 1016

1.25

2.2 × 1017

820

8.9 × 1010

200

180

2.5 × 1016

1.47

5.5 × 1016

1260

1.5 × 1011

equations can be used, namely Eq. (2.21). Next, we use the measured electron density ne

for a given set of PW conditions to determine how many electrons (per unit volume) exist

per energy, corresponding to this initially Maxwellian EEDF, so that for a bin at energy E

and width ∆E:

neb(E) = nef (E)∆E .

(3.5)

The volumetric occurrence rate at which a given inelastic process results from collisions with

electrons within this energy bin at energy E is given by:

(cid:114) 2E

me

Ru(E) = neb(E)ngrd

σ(E) .

(3.6)

The symbol Ru denotes that this is the upper bound of the rate because it assumes that

the EEDF initially is a Maxwellian shape. The ground-state density ngrd as mentioned

previously is approximately the neutral density nn, f (E) is the EEDF value, and σ(E) is

the cross section for the inelastic process. We assume that these energy bins are fine enough

that the EEDF doesn’t significantly change from one to an adjacent one, and they are indeed

constructed that way for the analysis that follows. This we can compare with the volumetric

97

Figure 3.2: The ratio of inelastic process rates from ground state, to the electron-electron
collision rate neνee. The inelastic process rate is determined as a function of energy, so
that an occurrence is triggered only from electrons at energy E. On the other hand, the
electron-electron collision rate is the rate over the entire EEDF.

(Maxwellian-averaged) electron-electron collision rate neνee using Eq. (3.3), which is a mean

value over the whole EEDF. It would be more proper to compare instead the rate of energy

transfer via the inelastic process as well as electron-electron collisions which change the

participating electrons’ energies. This is necessary to consider because the high energy tail

would actually be re-populated more slowly than the overall electron-electron collision rate

would suggest because most collisions between a high energy electron and any other electron

will result in the former losing energy rather than gaining. This method is incorporated in

98

10152025301E-111E-101E-91E-810152025301E-121E-111E-10Ratio: Inelastic Rate / el-el Collision RateEnergy [eV] Grd-excited e-impact reaction Grd-ion e-impact reaction Combination of both processesHelium, Te = 2.00Argon, Te = 1.47Energy [eV]Boltzmann solvers, as is mentioned below.

The ratio of these two volumetric process rates is shown in Fig. 3.2 for both a helium case

and an argon case, corresponding to the set of operating conditions He OC2 and Ar OC2

identified in Tab. 3.1. From this it can be seen that within a unit volume the combined -

considering excitation to the lowest-lying excited state as well as ionization, both from ground

state - inelastic process rate is at least 8 orders of magnitude lower than the electron-electron

collision rate taken over the entire EEDF in helium and at least 9 order of magnitude lower

in argon, suggesting that we could expect only a minor deviation from Maxwellian shape.

Cross section data for the inelastic processes examined were obtained via Ref. [54] for

helium and via Refs. [102, 103] for argon. The inelastic process rates are many orders of

magnitude lower than the electron-electron collision rate, we expect that the plasma in the

PW is well-described with a Maxwellian EEDF. It must be noted that the measured electron

density and temperature which this Maxwellization test relies upon are likely the values close

to the center of the plasma. Towards the edge, we expect a much reduced electron density,

a somewhat reduced electron temperature and heavy temperature, and a therefore much

increased ground state density [81]. However, since the central region is expected to be the

region where emissions primarily originate from, potential departure from Maxwellian EEDF

is less consequential in the outer edges of the arc.

Another point to note is that Boltzmann solver models such as BOLSIG+ can also be

used to conduct in a more detailed fashion the type of analysis illustrated in this Section [104].

This model assumes a spatially uniform plasma (over the scale of the collisional mean free

path) that is also steady-state. These assumptions should be adequate for studying the core

of the PW arc. Using initialized cross sections for collisional processes of interest,the code

99

Figure 3.3: Results of BOLSIG+ calculations by applying the operating conditions for He
OC2 and Ar OC2 in Tab. 3.1. Shown also are the effective electron temperatures. Dotted
lines are the EEDFs solved for by BOLSIG+ and solid lines are the corresponding Maxwellian
EEDFs whose electron temperature Te matches the effective temperature Tef f of the dotted
line EEDF.

solves the Boltzmann equation, given by:

∂f
∂t

+ v · ∇f − e
me

E · ∇vf = C[f ] ,

(3.7)

in which f is the electron distribution in six-dimensional phase space, v the velocity coor-

dinates, e and me are elementary charge and electron mass respectively, E is the electric
field, ∇v is the velocity-gradient operator, and finally C[f ] represents the rate of change in

100

0510152025303540-10-9-8-7-6-5-4-3-2-10Teff = 1.69 eVlog10(EEDF [1/eV])Energy [eV] Modeled Argon EEDF Corresponding Maxwellian___________________________ Modeled Helium EEDF Corresponding MaxwellianTeff = 2.43 eVdistribution f resulting from collisions (of all types) [104].

Applying the BOLSIG+ model to test cases for the PW, using the same parameters

indicated in Tab. 3.1, we can examine the steady-state EEDF shape relative to a pure

Maxwellian one. The results for the same operating conditions examined previously - He

OC2 and Ar OC2 from Tab. 3.1 - are shown in Fig. 3.3. From this it is clear that there

is some modest deviation from Maxwellian shape at the higher energy values. For the work

in this thesis however, we shall proceed through analyses assuming that the EEDF is close

enough that it may be considered Maxwellian.

3.2 Collisional-Radiative Model (HeCRM)

As mentioned in Section 2.2.3, electron temperature in the helium plasma window arc can

not so easily be obtained via a Boltzmann plot as it can in the case of argon. A collisional-

radiative model is necessary to compare modeled and measured relative emission intensities,

to determine the electron temperature. This model involves calculating densities of the

numerous excitation and ionization states found in the plasma [105].

The transient behavior of a given state’s density nk is given by:

(cid:88)

Rpop −(cid:88)

dnp
dt

=

Rdepop ,

(3.8)

in which Rpop and Rdepop broadly are the rates by which that state’s population increase

and decreases respectively. Including all possible population-changing mechanisms except

spatial removal mechanisms (diffusion), this becomes:

101

= −n(p)

dnp
dt

A(p, q) + ne

C(p, q) + neS(p)

(cid:35)

(cid:35)
n(p)B(cid:48)(q, p)

(cid:88)
(cid:34)

q<p

(cid:35)

(cid:34)(cid:88)
(cid:34)(cid:88)

q<p

+

q>p

(cid:88)

q(cid:54)=p

(cid:88)

q(cid:54)=p

n(q)A(q, p) +

n(q)C(q, p) +

+ nine

neα(p) + β(p) + βd(p)

.

(3.9)

With this notation, q < p indicates level q is higher than p and (p, q) indicates the process

goes from state p to state q. Changes in state can be from spontaneous photon emission with
rate A, photon absorption with rate B(cid:48), electron-impact excitation or de-excitation with rate

C, ionization with rate S, three-body recombination with rate α, radiative recombination

with rate β, and dielectronic recombination with rate βd. This symbolism is taken from that

of Refs. [14, 15], in which a CR model for singly-ionized helium plasma is applied. This is

the same CR model which we will utilize here to analyze the helium plasma window. Only

a limited description of this model will be given here and the reader is referred to the above

referenced works and references therein for more extensive details of the inner workings of

their CR model, called the HeCRM. In our application of this model, we will exclude the
photon absorption terms whose rates are given by B(cid:48), for reasons of dramatically simplifying

the application of the model, since the radiation trapping effect is non-local and takes into

account the spatial distribution of the states.

In what T. Fujimoto in Ref. [15] and M. Goto in Ref. [14] call Formulation II, all states

are considered to be in a quasi-steady-state condition with the left-hand-side of Eq. (3.9)

being 0, with the exception of the neutral ground state and ion state. In this formulation,

after a great deal of algebraic manipulations, Eq. (3.9) for all of the excited states other than

102

the neutral ground and ion states can be expressed as a sum of two terms, one proportional

to the neutral ground state population and one proportional to the ion state population.

Each state’s population can then be given by:

n(p) = R0(p)neni + R1(p)nengrd ,

(3.10)

in which now all the state-coupling rates are now wrapped up into two reduced population

coefficients R0(p) and R1(p). The term proportional to ion density ni signifies transitions

moving downwards in energy, and the term proportional to the ground state density ngrd

signifies transitions moving upwards in energy [106]. To understand specifically how these

population coefficients include all of the different rates presented in Eq. (3.9), the reader is

again referred to Refs. [14, 15]. These population coefficients are functions of the state p as

well as both electron density ne and electron temperature Te. Thus the system of equations

for densities of every excited state can be obtained for a specified ne and Te and with this

synthetic excited state population distribution also obtain a synthetic emission intensity

spectrum. The relationship between the emitting state densities n(p) and the corresponding

emission intensities was given by Eq. (2.22). Dropping the geometric factor in that equation,

the synthetic emission intensity for an emission from state p to state q is:

Is(p, q) = n(p)A(p, q)∆E(p, q) ,

(3.11)

where ∆E(p, q) is the energy of the photon emitted in the de-excitation process. Note that

since this doesn’t include any geometric factors, the intensity scale is arbitrary. In practice,

what is done for the present work is to initialize the HeCRM with electron density ne as

measured via Stark broadening, and assume quasineutrality so ni = ne. Additionally, a

103

value for the ground state density ngrd is required. It will be assumed at this point that

the ground state constitutes the vast majority of the un-ionized species so that the ground

state density is essentially the neutral density nn which by using Dalton’s law of partial

pressures (which will be more thoroughly introduced in the next section) in Eq. (3.17), can

be expressed as:

(cid:16)

(cid:17) − ne .

Pp − nekTe

ngrd ≈ nn =

1
kTh

(3.12)

Since the heavy particle temperature Th in Eq. (3.12) is not known via measurement,

and is only calculated through the 1D analysis that will be described in Section 3.3, which

itself depends on the electron temperature value Te, we must rely on an alternative method

to obtain ngrd for the HeCRM. This alternative method will be to use the PLASIMO arc

modelling package that will be thoroughly described in Section 3.5 to determine the neutral

density nn and equate with ngrd.

Everything is now in place to initialize the HeCRM using modeled values of ground

density ngrd, electron density ne, and a set of test electron temperature values, which will

be identified as Tt. So, for each Tt there will be a synthetic spectrum created to quantitatively

compare with the measured one. To conduct such a comparison, the first step is to obtain

(with a given Tt) for each emission the ratio of synthetic to measured intensity to obtain a
set of ratios {R(Tt)}. For a synthetic spectrum that perfectly matched the measurement,
each emission member of the {R(Tt)} would be the same value, so we want to determine the

degree of relative deviation from this ideal simulation case.

A straightforward technique to do so is by determining which test temperature Tt gives the

minimum coefficient of variation (ratio of standard deviation to mean) for that temperature’s

104

Figure 3.4: Matching Parameter for HeCRM synthetic spectra compared to measured spec-
tra of a 200 torr GCS pressure, 120 A arc in 6x6mm PW geometry, at two measurement
locations. The model was initialized for P2/6 with ne = 2.0 × 1015 cm-3 and ng = 1.1 × 1017
cm-3, and for P6/6 with ne = 1.5 × 1015cm-3 and ng = 6.6 × 1017cm-3 (ne from measurement
and ng from PLASIMO model).

105

0.00.51.01.52.02.53.00.00.10.20.30.40.50.60.70.8HeCRM Matching ParameterTest Temperature [eV] Observation at P2/6 Observation at P6/6Selected as Electron Temperaturecorresponding set {R(Tt)}, which will be referred to from now on as the Matching Parameter

(MP). This is the test electron temperature which generates a synthetic spectrum that

best reflects the measured spectrum, and this temperature will be deemed the real electron

temperature Te. The HeCRM was used with a similar though slightly different analysis

procedure in a test case discussed in Ref. [14], again to determine electron temperature (and

density in that case) from a set of experimental emission intensities. A figure illustrating the

process used in the present work is shown in Fig. 3.4. This result is for a He 6x6mm PW,

with GCS pressure of 200 torr and arc current of 150 A, observed both at P2/6 and P6/6.

An interesting feature that results from this analysis technique is that there are in fact

two local minima of MP values, and so two best-fitting Tt values, which we identify as Tlo

and Thi. The lower of these temperatures, like the measured excitation temperature Texc, is

seemingly too low to sufficiently result in ionization throughout the channel. A comparison

of measured and synthesized emission intensities at both the Tlo and Thi is given in Fig.

3.5. Therefore it is the higher matching temperature which is identified as the electron

temperature in helium.

3.3

1D Model

The goal of this section is to assess what is most impactful in establishing the PW’s mass

flow and understanding the nature of its reduction from that of a corresponding non-arc gas

flow. The procedure in analyzing the momentum-balance equation is similar to that used in

Refs. [41, 107], although the various authors utilize the transport equations given in Section

1.2 by taking different transformations and assumptions, e.g.

in Refs. [39, 108–110]. The

106

Figure 3.5: Measured and synthesized irradiances corresponding to the selected both the
lower and upper matching temperature values in Fig. 3.4 (Tlo and Thi). The temperature
Thi is selected as the electron temperature.

107

37540042545047550052502468101214163754004254504755005250123456 Measured Intensities Synthesized Intensities using Tlo Synthesized Intensities using ThiMeasured IntensitiesWavelength [nm]Plate 2/6Plate 6/6Wavelength [nm]behavior of the mass flow ˙m will be investigated using the momentum balance equation:

(mnaua) + nam(ua · ∇)ua + ∇Pa + ∇ · ↔

π − qna(E + (ua × B)) = Sm .

(3.13)

∂
∂t

3.3.1 Overall Momentum Balance

We will focus on the momentum balance equation which can be analyzed to obtain an

expression for mass flow in terms of other properties. We will start by summing (3.13) over

each species in the arc channel: neutrals, ions, and electrons. Due to their light mass, the

electrons won’t appreciably contribute to mass density or flow velocity due to their minute

mass compared to the neutrals and ions. The result is:

mn(u · ∇)u + ∇Pp + ∇ · ↔

π = 0 ,

(3.14)

where the total plasma pressure is Pp, u is the hydrodynamic velocity, essentially the heavy

particle flow velocity uh given by:

uh =

˙m

mhAnh

ˆz ,

(3.15)

where nh is heavy particle density, A is channel area, and mh is heavy particle mass. There

is no flow in the radial direction throughout the arc channel, so taking only the z-component

of the flow velocity is justified, and this also means that plasma pressure Pp is constant

with respect to radius at any axial position. It is furthermore assumed all the properties

are axisymmetric, and no angular-dependence exists for any variables. A relation can be

obtained between heavy particle density nh and total plasma pressure Pp by invoking an

108

equation of state as Dalton’s law of partial pressures, which assumes each species of the

plasma (electrons, ions, and neutrals) each obey an ideal gas law, such that:

(cid:88)

a

Pp =

nakTa ,

(3.16)

As alluded to earlier in Section 1.2, it is assumed that both neutrals and ions possess

approximately the same temperature, deemed simply as heavy particle temperature Th. As

it was mentioned in Section 1.2 and is conveyed in Ref. [41], this is a reasonable assumption

because the energy-exchange in collisions of like-mass particles is much more efficient than

collisions between a neutral or ion and an electron due to the mass disparity. In this case

then, a quasineutral plasma with electrons, ions (charge state 1 only), and neutrals, Eq.

(3.17) can be expressed as:

Pp = Ph + Pe = nhkTh + nekTe = (nn + ne)kTh + nekTe .

(3.17)

From this, the heavy particle density nh can be obtained as:

nh =

Pp − nekTe

kTh

.

(3.18)

One can also obtain the ionization degree α, the ratio of ions to heavy particles (assuming,

as always, quasineutrality so ni = ne) as:

α =

nekTh

Pp − nekTe

.

(3.19)

109

The stress tensor

↔
π for the plasma has components given by:

(cid:32)

(cid:33)

παβ = −η

∂uα
∂xβ

+

∂uβ
∂xα

− 2
3

δαβ∇ · uh

.

(3.20)

The last term of Eq. (3.14) is the viscous term and intrinsically relies on radial behaviors as

well as axial, so to apply it in this 1D simplification, we will average its value over the channel

radius. The components of the stress tensor

↔
π are given by Eq. (3.39), so the z-component

of the tensor-divergence is:

(cid:16)∇ · ↔
(cid:17)

π

∂πrz
∂r

+

1
r

∂πφz
∂φ

+

∂πzz
∂z

+

πrz
r

.

=

z

(3.21)

Ignoring the φ-dependent term, using the components of Eq. (3.39) in Eq. (3.21), the viscous

term becomes:

(cid:16)∇ · ↔
(cid:17)

π

z

(cid:34)

= −

∂η
∂r

∂uz
∂r

+ η

∂2uz
∂r2

(cid:35)

(cid:34)

− 4
3

∂η
∂z

∂uz
∂z

+ η

∂2uz
∂z2

(cid:32)

(cid:35)

−

(cid:33)

.

η
r

∂uz
∂r

(3.22)

Lastly, we will relabel the average of this viscous term for brevity, defining the term as G,

where the angle brackets signify that it is an average over the channel radius:

G ≡ (cid:104)(cid:16)∇ · ↔

π

(cid:17)

(cid:105) .

z

(3.23)

The role of viscosity is different than that used in Refs. [41, 107], in which the viscosity

term ∇ · ↔

π is taken to be 1

2 ρu2 f

D where friction factor f represents friction with the wall

and ρ is the plasma’s mass density. This means that the only term retained from Eq (3.22)

(cid:17)

(cid:16) η

r

was the

∂uz
∂r

term in their work. However, empirically it appears that for the plasma in

110

the PW, each term within Eq (3.22) is significant relative to the others, so dropping any of

them cannot be justified.

The aim now is to establish an expression for the mass flow in the plasma using these

previous equations. After some algebra, Eq. (3.14) can be rearranged to give:

mnuu(cid:48) + P(cid:48)

p + G = 0 .

(3.24)

From here, the next step is to re-express the velocity uh and its derivative in terms of the

mass flow. Here, primes represent axial derivatives, so in the z-direction. Using Eq. (3.15)

and taking its axial derivative as:

u(cid:48)
h = − ˙m
mhA

n(cid:48)
h
n2
h

.

(3.25)

Now, plugging Eq. (3.15), (3.25), and (3.22) into Eq. (3.24), we end up with an equation

for the mass flow ˙m:

(cid:118)(cid:117)(cid:117)(cid:116)mA2

(cid:32)

(cid:33)(cid:16)

n2
h
n(cid:48)

h

(cid:17)

P(cid:48)
p + G

.

˙m =

(3.26)

It is worth pointing out that both n(cid:48)

h and P(cid:48)

p will be negative in sign. The latter is

obvious; the pressure must decrease along the direction of flow because this pressure change

is what establishes the flow in the first place. The former is not as immediately obvious, so

to elucidate we differentiate nh in Eq (3.18) to give:

(cid:16)

n(cid:48)
h =

−T(cid:48)
h
kT 2
h

Pp − nekTe

+

1
kTh

(cid:17)

(cid:16)

p − (nekTe)(cid:48)(cid:17)

P(cid:48)

.

(3.27)

Here, we note that since we expect Th to generally rise as the gas moves down the channel,

111

T(cid:48)
h will be positive and since we mentioned above P(cid:48)
Eq. (3.27) which can be positive is the −(nekTe)(cid:48) ≡ P(cid:48)

p is negative in sign, the only term in

e, where we note that by Dalton’s law

of partial pressures we can just define this electron pressure axial derivative. Empirically, it

seems that this the electron pressure doesn’t change substantially because while Te generally

increases as we move down the channel’s length, ne generally decreases.

We can now more clearly understand what is contributing to reduced mass flows observed

in the PW. We see that the heavy density and its axial derivative, nh and n(cid:48)
role. The rate of pressure drop P(cid:48)

p and the viscous term G also play a part, but we see that

h, play a large

it’s possible only one really contributes if the other is small relative to it. We therefore will

seek to compare the values of these terms, with results presented in Section 4.2.6.

There is one more consideration regarding the effect of viscosity on the flow, which is the

contribution of viscous heating of the heavy particles, compared to other heating mechanisms.

This is necessary to understand because the heating influences the behavior of the heavy

particle density nh and its derivative which are factors in Eq. (3.26). These factors appear

in energy balance equation first mentioned in Section 1.2, and restated here as:

(cid:32)

∂
∂t

(cid:33)

+ ∇ ·(cid:16)3

2

3
2

nakTa

(cid:17)

nakTaua

π · ∇(cid:17)
(cid:16)↔

+ nakTa∇ · ua +

u + ∇ · Q = SE .

(3.28)

From this, an expression for the energy balance of heavy particles in particular is given

as:

(cid:32)

3
2

∇ ·

(cid:33)

nhkThuh

+ nhkTh∇ · uh = Se + Qv − ∇ · qh − Qrad .

(3.29)

Terms on the left side of this equation represent the kinetic energy terms (thermal and

112

flow) of the flowing plasma, and the terms on the right side represent the source terms.

Of these, Se is the external energy source term which here is the energy obtained through

collisions with more energetic electrons, Qv is the energy generated from viscous dissipative
heating, ∇·qh is the heat flux term through conduction, and Qrad is the term for energy lost

due to radiation. In this work, only this last term will be assumed insignificant compared to

the others and dropped. An additional note that will not be considered here is mentioned

in Ref. [111] is that an additional energy source term could be added related to the energy

of chemical reactions or inelastic collisions between the heavy particles. In this thesis, the

primary reason for bringing up Eq. (3.29) and its terms is to provide context for the viscous

heating term Qv and the term to which it will be directly compared, the electron heating

term Se.

For the source term Se, also referred to as the energy exchange term since it is the electron-

to-heavy energy exchange rate per unit volume, we must note that the energy exchange is

essentially uni-directional, causing the heavy particle temperature Th to ever approach the

electron temperature Te [28]. This term is given by:

Se =

3
2

2me
mh

neνehk(Te − Th) ,

(3.30)

where me and mh are the electron and heavy particle mass respectively, ne is the elec-

tron density, Te and Th are the electron and heavy particle temperatures, and νeh is the

momentum-transfer collision frequency between electrons and heavy particles, which is the

sum of electron-neutral and electron-ion momentum-transfer collision frequencies:

νeh = νen + νei .

(3.31)

113

The collision frequency between a projectile species and a target species ntar particles is

defined as:

ν = ntar(cid:104)vrσcs(cid:105) ,

(3.32)

where σcs is the interaction cross section between pair of particles under consideration and vr

is the relative velocity of the two particles, and the angular brackets denote that this is taken

as an average over collision speeds. Momentum transfer collision frequency is defined as the

frequency with which a given species has its momentum deflected by 90 degrees, either via a

single collision or by successive smaller-angle collisions. Energy exchange between electrons

and heavy particles slower by a factor of 2me
mh

heavy temperature often exists [28, 29].

. This is why a disparity between electron and

To make use of Eq. (3.30) for this calculation requires a connection between the electron-

heavy elastic collision frequency νeh and measured quantities. This connection can be estab-

lished through the plasma’s electrical conductivity σ, a property which can be ascertained via

measurement of the cascaded plate floating voltages of the plasma’s enclosure as described

in Section 2.1. To do so, take the electrical conductivity to be defined based on:

j = σE ,

(3.33)

where j is the current density and E is the electric field. We then can equate Eq. (3.33)

with an alternative expression for the current density being related to electron drift velocity

vd,e and electron density ne, namely:

j = vd,eene .

114

(3.34)

Next we need to express the electron drift velocity vd,e in terms of the collision frequency

νeh. This drift velocity is obtained by integrating the force on the electron in the field E

over a time equal to the inverse of the collision frequency. In the axial direction, this axial

velocity is then given by [28]:

vd,e =

eEz
νehme

.

Inserting Eq. (3.35) into Eq. (3.34) and equating with Eq. (3.33), we obtain:

νeh =

e2ne
σme

.

Finally then, we obtain a useful expression for the electron heating term:

(cid:16)

Te − Th

(cid:17) e2ne

σ me

.

Se =

3me
mh

nek

(3.35)

(3.36)

(3.37)

For the next term in to work out in Eq. (3.29), the viscous heating term Qv, recall the

expression from the full 3D energy balance equation Eq. (1.8), in which the viscous heating

term Qv is the part of the equation given by:

(cid:16)↔
π · ∇(cid:17)

uh =

(cid:88)

β

Qv =

πzβ

∂uz
∂β

,

(cid:32)

where

↔
π is the stress tensor, whose components are given by:

παβ = −η

∂uα
∂xβ

+

∂uβ
∂xα

− 2
3

δαβ∇ · uh

(3.38)

(3.39)

(cid:33)

,

in which η is the viscosity, and x is just a spatial coordinate. The procedure used to determine

115

the value of the viscosity η itself will be outlined in Section 3.4, but it’s sufficient here to say

that it is a function of both heavy temperature Th and ionization degree α. Applying this to

Eq. (3.38) gives the form of the viscous heating term which can be inserted into Eq. (3.29):

π · ∇(cid:17)
(cid:16)↔

Qv =

uh = η

(cid:34)

(cid:32)

(cid:33)2

(cid:32)

(cid:33)2(cid:35)

1
2

∂uz
∂r

+

4
3

∂uz
∂z

.

(3.40)

Now, expressions for both the electron heating term Se and the viscous heating term Qv

have been obtained. As with the relative terms in the mass flow equation Eq. (3.26), these

two heating contributions will be compared in Section 4.2.6, with the viscous heating term

taken as an average over the channel radius as it was for the mass flow equation.

3.4 Viscosity

In the previous sections, the viscosity played an important role in the evolution of the heavy

particle temperature Th, and by extension the heavy particle density nh, ionization degree

α, and mass flow ˙m. Viscosity is a fluid friction property that effects the rate of flow through

a channel, with greater viscosity results in a lower mean flow velocity. Hirschfelder, Curtiss,

and Bird developed the kinetic theory by which the transport coefficients - viscosity, diffusion,

and conductivity - can be determined in any pure gas or multi-component mixture, including

those with charged particles interacting under Coulomb potentials [112]. As a result, this

kinetic theory will be used to calculate viscosity in the plasma window as a function of

calculated values. Particularly, the heavy particle temperature Th and ionization degree α

are critical values that impact the viscosity; greater temperature increases viscosity, while

greater ionization degree decreases it. We will need the previously obtained a useful form of

116

the ionization degree α:

α =

nekTh

Pp − nekTe

,

(3.41)

where ne is the electron density, k the Boltzmann constant, Th the heavy particle tempera-

ture, Te the electron temperature, and Pp the total plasma pressure.

It is through collision integrals that the dynamics of collisions enter into the determination

of these transport coefficients [112]. These collision integrals, whose type is identified by l

and s, are defined as:

(cid:115)

(cid:90) ∞

0

kT
2πµij

Ω

(l,s)
ij =

e−γ2

γ2s+3Q(l)(g)dγ ,

(3.42)

with the cross section for a collision of type l given by:

(cid:90) ∞

Q(l)(g) = 2π

(1 − cosl(χ)bdb ,

(3.43)

and

0

(cid:90) ∞

rmin

χ(g, b) = π − 2b

(cid:114)

1 − b2

dr/r2
r2 − φ(r)
1
2 µij g2

.

(3.44)

Eq. (3.44) is the angle of deflection in a collision governed by potential φ(r) and impact

parameter b. The unitless parameter γ is defined as:

γ2 ≡ µijg2
2kT

=

E
kT

,

(3.45)

in which µij is the reduced mass of species i and j, g the relative velocity between them,

117

and so E is just their kinetic energy.

In this work, relevant cross sections (Q(l)) have been obtained from the literature, as a

function of collision energy. For argon, cross section information was obtained from Ref. [113]

and for helium it was obtained from Ref. [114]. As a result of these being in terms of collision

energy, it is desirable to re-express (3.42) as a function of energy E instead of γ. Doing so

yields:

(cid:115)

(cid:90) ∞

1

8πµijkT

0

(cid:33)s+1

(cid:32)

E
kT

e−E/kT

Ω

(l,s)
ij =

Q(l)(E)dE .

(3.46)

With the framework of the collision integrals established, they can now be put to use in

determining viscosity. The first step to doing that is to calculate the viscosity correspond-

ing to a pure substance, considering each member of the mixture in isolation. The first

approximation to the viscosity for a pure substance, is [112]:

[ηii]1 =

5
8

kT
(2,2)
ii

Ω

.

(3.47)

Now, beginning with ions and applying the above set of equations to particles interacting

under a Coulomb potential, we obtain:

(cid:34)

(cid:18)

Q

(2)
C (E) = 4πb2
0

ln

1 +

(cid:17)2(cid:19)

(cid:16) λD

b0

− (λD/b0)2
1 + (λD/b0)2

(cid:35)

,

(3.48)

in which, for nonisothermal and quasineutral plasma with only singly ionized particles

present, the Debye length from Section 1.2 is:

(cid:115)

λD =


0kTe
e2ne

,

(3.49)

118

and the parameter b0 is known as the classical distance of closest approach, given by [5]:

b0 =

e2

4π
0µg2 =

e2

8π
0E

.

(3.50)

This expression for the cross section is then substituted into Eq. (3.47) to obtain the vis-

cosity associated with the particles interacting via the Coulomb potential. Note that in Eq.

(3.46), the presence of

√
µij in the denominator implies that collisions between electrons will

contribute much less to the viscosity than will collisions between ions. As a result, in this

work, electron contributions to viscosity will be neglected, and calculations for the overall

viscosity of the plasma fluid will be obtained by considering it as a mixture of neutrals and

ions.

The next piece necessary is a quantity denoted by [η12]1. The 1 outside the brackets

identifies that this is for the first approximation (higher order approximations are not em-

ployed in the present work), and as per the description in Ref. [112], this quantity can be

regarded as the coefficient of a hypothetical pure substance that interacts in the manner

species 1 and 2 do. For simplicity, it is assumed that the neutral-ion collisions also interact

with the neutral-neutral collision cross section, which as mentioned previously are obtained

from Refs. [113] and [114] for argon and helium respectively. As a result of the above as-

sumption that the neutral-ion collisions are essentially the same as the neutral-neutral ones,
we will treat [η12]1 ≈ [η11]1 in this work.

For a binary mixture, the overall fluid viscosity depends upon the relative molar fractions

and molecular weights of the two species as well as the viscosities of the corresponding pure

substances. Adopting the notation used by the authors, species 1 denotes neutral, and

species 2 denotes ion. The 1 outside of the brackets denotes the first approximation [112].

119

Thus:

,

[ηmix]1 =

1 + Zη
Xη + Yη

Xη =

x2
1

[η11]1

+

2x1x2
[η12]1

+

x2
2

[η22]1

,

(3.51)

(3.52)

(cid:40)

(cid:33)

(cid:32)

M1
M2

x2
1

[η11]1

+

2x1x2
[η12]1

(cid:32)

Yη =

A∗

12

3
5

(cid:33)(cid:32)

[η12]2
1

(M1 + M2)2

4M1M2

[η11]1[η22]1

(cid:33)

(cid:33)(cid:41)

,

(cid:32)

M2
M1

+

x2
2

[η22]1

(cid:33)

(cid:40)

(cid:32)

x2
1

M1
M2

Zη =

A∗

12

3
5

(cid:34)(cid:32)

+ 2x1x2

(M1 + M2)2

4M1M2

(cid:33)(cid:32)

[η12]1
[η11]1

+

[η12]1
[η22]1

(cid:33)

(cid:35)

− 1

(cid:32)

+

x2
2

M2
M1

A∗
12 =

2
3

Ω(2,2)
Ω(1,1)

.

(3.53)

(cid:33)(cid:41)

,

(3.54)

(3.55)

As mentioned at the beginning in this section, the viscosity depends primarily on heavy

particle temperature Th and ionization degree α. The relationship with the heavy particle

temperature is a result of transmitting momentum of the flow towards the walls of the chan-

nel, and the relationship with the ionization degree is a result of the molar fraction of the

mixture constituents in Eq. (3.51) and the fact that the pure-substance-viscosity terms are

governed by different potentials depending on if they’re neutrals or ions. Electrons contribute

relatively little to viscosity due to their low mass and relative inability to affect the momen-

tum of the heavy particles which transmit almost the entirety of the mass flow. This, again,

120

Figure 3.6: Argon plasma viscosity calculated using Chapman-Enskog kinetic theory de-
scribed above. Viscosity values are calculated at three different ionization degrees to illustrate
their impact. The black curve is that obtained by Murphy and Arundell [13] in which the
assumption of Saha ionization equilibrium is taken.

is the reason electron effects are neglected in determining viscosity in the present work. Often

when plasma viscosity is reported, it is under the assumption of Saha ionization equilibrium

and Te = Th, so that ionization degree α and Th are both functions of electron temperature

Te,to establish a convenient relationship between the temperature and the electron density

(and ion density, following assumption of quasineutrality) [13, 115]. Saha excitation equi-

librium was discussed briefly in Section 2.2.3.1, and Saha ionization equilibrium is similar

except rather than applying to excited levels, it applies to two adjacent ionization stages.

121

05000100001500020000250000102030405060Argon Plasma Viscosity [10-5 Pa*s]Heavy Particle Temperature [K] Ionization degree  = 0.001  = 0.045  = 0.18 Murphy and ArundellHowever, Saha ionization equilibrium generally requires much higher electron densities than

those attained in the PW, and is not a justifiable assumption to make in this case. Figure

3.6 illustrates viscosity in argon as a function of heavy particle temperature Th at several

ionization degrees α. Also in this figure is a previously reported calculation of argon plasma

viscosity calculated by Murphy and Arundell [13], in which Saha ionization equilibrium is

implicit. As a result, their calculation is a function only of temperature.

3.5 Plasma Simulation Model - PLASIMO

PLASIMO (plasma simulation model) is a plasma modeling package developed by the group

for Equilibrium and Transport in Plasmas at Eindhoven University of Technology [111,116].

There are many different model packages that PLASIMO supports depending upon the type

of plasma under consideration [116, 117], but the package under consideration in the present

work is designed for axisymmetric arc plasmas [111]. It is used to compare modeled properties

with corresponding measured ones, and is investigated as a possible tool to assess plasma

window arrangements and conditions otherwise not investigated or accessible through the

course of this thesis work.

To gauge the reliability of this model in approximating the plasma window under spec-

ified operating conditions, several modeled plasma and flow properties can be compared to

their measured counterparts determined experimentally on the NSCL plasma window test

stand. These include gas pressure, electric field, electron temperature, electron density, and

wall heating, results of all of which are presented and discussed in 4.2. If all relevant physics

has been included in the model, the boundary conditions selected appropriately, and the

properties mentioned above are relatively comparable to the experimental values, it is con-

122

jectured that the other properties such as viscosity η and heavy particle temperature Th

which are not easily determined experimentally can be estimated using the model’s values.

This then could be used in determining importance of these properties in limiting the gas

flow, following the framework for obtaining an expression for mass flow ˙m in Section 3.3.

Because the plasma window study is focused on a cascaded arc arrangement, PLASIMO’s

arc package is the one that will be discussed from this point forward. This foundation of

this model relies upon the distinction between fast and slow plasma interactions. Fast

interactions (order of 10-8 s) are kinematic (collisional) and radiative processes, and the

slower ones (order of 10-3 s) are fluid interactions, such as convection, conduction, and

diffusion. As a result, plasma is considered a fluid, within which at every location plasma

parameters can be defined. In addition to this, the model makes several assumptions about

the plasma flow [111]:

1. the flow is considered laminar

2. the flow is stationary (no time variation)

3. the plasma is axisymmetric

4. the principle of quasineutrality is upheld

5. there are two temperatures - Te characterizing electrons and Th characterizing the

heavy particles, and these two temperatures need note be equal

6. kinetic energy distributions are all considered to be Maxwellian

7. sheath-associated mechanisms are disregarded

Radiative energy transport via absorption and re-emission is not considered, nor are the

occupations of the excited states of neutrals or ions. The plasma is considered to consist of

123

just ground state neutrals, ground state ions, and electrons. However, the excited neutral

states are accounted for in an indirect manner by inclusion of step-wise ionization rates, in

the form:

e + A ←→ e + A∗ ,

e + A∗ ←→ 2e + A+ .

(3.56)

(3.57)

This step-wise ionization process would occur in addition to direct ionization of the un-

excited neutrals to the ionized state (only the first ionization stage is considered in the
PLASIMO models of both argon and helium). In these reactions, A∗ is an effective excited

species. A collisional-radiative model must be utilized to determine what the effective ion-

ization rate from the collection of real excited states as a function of temperature. The argon

PLASIMO model employs a step-wise ionization rate using results of Ref. [118], namely:

(cid:112)
Ksi = (7.314 × 10−15)

Teexp(−12.06/Te) [m3/s] ,

(3.58)

where Te is given in eV.

The step-wise ionization process in helium was determined using a combination of HeCRM

(described in Section 3.2) and ionization rates from metastable excited helium states, ob-

tained in Ref. [119]. Since the PLASIMO model was not set up with explicit excited species

present, it was necessary to use the HeCRM to ascertain the expected behavior of the

metastable density as a function of electron temperature Te. As a result, two step-wise

ionization channels were included for the helium PLASIMO model, through the metastable

124

states 1s23S and 1s21S. These are given in Eqs. (3.59) and (3.60) as:

Ksi,1 = (1.21 × 10−20)T 5.66

e

exp(0.273/Te) [m3/s] ,

Ksi,2 = (9.18 × 10−22)T 5.99

e

exp(−1.132/Te) [m3/s] .

(3.59)

(3.60)

In these two equations, Te is in units of eV. These rates should only be applied for electron

temperatures Te close to the values under investigation here for the PW, around 2-3 eV.

Maxwellian velocity distributions are assumed for each particle species, and PLASIMO

employs the continuity equations from velocity moments of the Boltzmann equation, as

described in Section 1.2, with Eq. (1.6), (1.7), and (1.8). As described in Ref. [111], in

PLASIMO’s arc model the characteristic temperatures are allowed to differ between heavies
(ions and neutral particles) and electrons, so Th (cid:54)= Te. As a result, energy balance of the

plasma exists in two equations, one for electrons and one for heavies. These are, respectively:

∇ · (ρe
eu) + Pe∇ · u + ∇ · qe = QOhm + Qe

(3.61)

,

and

∇ · (ρh
hu) + Ph∇ · u + ∇ · qh =

↔
π : ∇u + Qh .

(3.62)

In these equations, u is the plasma bulk velocity:

(cid:88)

α

u =

(cid:88)

(nαmαuα)/

α

125

(nαmα) .

(3.63)

Due to their much smaller mass, electrons do not appreciably contribute to this velocity.

Also in these equations, ρ is mass density, 
 is the thermal energy per unit mass, P is the

species pressure,

↔
π is the viscous stress tensor, Qe and Qh denote energy gain or loss for

electrons or heavies respectively due to inelastic collisions or chemical processes, and QOhm

is the Ohmic heating term. For mass continuity and momentum balance, the equations are

summed over all particles, resulting in whole-plasma forms given by, respectively:

∇ · (ρu) = 0 ,

and

(∇ · (ρuu))i = −(∇P )i + (∇ · ↔

π)i + (j × B)i .

(3.64)

(3.65)

Additionally, the plasma equation of state is specified using Dalton’s law of partial pres-

sures in Eq. (3.17), with each species (electrons and heavies) obeying an ideal gas law in the

form P = nkT .

PLASIMO’s arc model will be generated in an axisymmetric configuration, so will be

2D, and excludes any rotational effects. A number of boundary conditions pertaining to

plasma properties will need specification. The general setup of these that will be applied

to the PLASIMO model of the plasma window are described in Table 3.5. These are speci-

fied according to cardinal directions, and the corresponding real boundary of each direction

is given in 3.5, along with some other abbreviations relevant to the boundary conditions.

These boundary conditions apply to the PLASIMO model used for a single-radius PW,

e.g. 6x6m. Other model geometries consisting of two-radii PW configurations such as

1x6mm 7x10mm have also been explored though require additional boundary conditions,

126

and tend to have more difficulty in achieving a converged solution, so the majority of the

results from PLASIMO will be focused on this basic single-radius system.

In these, the

model simplifies the geometry of the plasma window, and is a simple cylinder rather than

the ribbed structure of the true plasma window (since the metal plates and the insulators

between have different inner radii), and it lacks the discrete wall/insulator components, with

the model calculated voltage being a continuous drop from cathode to anode. So it could

be thought of as analogous to a plasma window comprised of infinitely many and thin metal

plates and insulators. Additionally, PLASIMO can not reliably model the unique plasma

characteristics of the cathode and anode fall regions [116, 120] (more information on these

regions can be found in e.g. Ref. [28]). The modeled region will be just the cascaded arc

region, from about the location of upstream edge of the first PW plate down to the upstream

edge of the anode, similar to the example studied in Ref. [111]. It was mentioned in Section

2.1 that metal plates are 7 mm thick and insulating pieces between are 2 mm thick. So the

modeled region for a PW consisting of 6, 8, or 10 plates will be 54 mm, 72 mm, and 90 mm

respectively. The meshing for the simple cylindrical PLASIMO model of a 6x6mm PW is

shown in Fig. 3.7. Any given model is run until an overall convergence of greater than 10-8

is achieved.

One thing to note is that since this modeled region is from the upstream edge of PW plate

1 to the upstream edge of the anode plate, the modeled region inlet and outlet pressures

will be obtained by extrapolating a linear pressure drop from two measured locations. The

two measurement locations for the 6x6mm PW configuration are plates 2 and 6, and for

the 8x6mm PW configuration is plates 2 and 8. The model’s exit pressure BC is a constant

Neumann value equal to the measured linear drop rate from the aforementioned two measured

locations. Some plate pressures for a 6x6mm PW are shown in Fig. 3.8 for both helium

127

Figure 3.7: Mesh used for the PLASIMO 6x6mm PW model, in which the “x [m]” axis
corresponds to the axial, or z-direction and the “y [m]” axis corresponds to the radial, or
r-direction. The cathode and gas entry side is the west edge and the anode and gas exit side
is the east edge, the north edge is the plasma-facing side of the enclosing metal plates, and
he south edge is the axis of symmetry. In the vicinity of the west, east, and north edges, the
mesh spacing is condensed for greater numerical stability.

128

Figure 3.8: Measured plate pressures in argon and helium arcs of a 6x6mm PW, expressed
as fraction of the GCS pressure. Plate pressures are given at the measured plate locations
of P2/6 (left) and P6/6 (right, note the change in ordinate scales). Linear extrapolation of
these pressures to the PLASIMO model region inlet and outlet provides the BCs used at
those locations.

and argon arc. The pressures shown in this figure correspond to P2/6 and P6/6, so a linear

extrapolation using these values is performed to the upstream edge of P1/6 and the anode

position to obtain the pressure BCs for the corresponding PLASIMO model.

By doing this, the model’s pressure boundary conditions end as just about 3% less than

the GCS pressure for the model’s inlet, and about 10% less than the measured plate 6

pressure for the model’s outlet.

It’s possible that the linear extrapolation doesn’t truly

represent the pressure drop in the plate 1 to plate 2 or the plate 6 to anode regions, but it’s

129

60901201501802100.7500.7750.8000.8250.8500.87560901201501802100.3750.4000.4250.4500.4750.5000.5250.550Solid = ArgonCenter Cross = Helium 150 torr 200 torr 250 torr 300 torr 350 torr 400 torrPlate Pressure (Fraction of GCS Pressure)Current [A]Plate 2/6Plate 6/6Current [A]Table 3.2: PLASIMO boundary conditions abbreviations.

Abbreviation Meaning
North

Plasma window enclosure (inner surface of cascade plates))

East

South

West

Temp

H.

Cst.

Dir.

Neum.

US

TIF

Cathode-side, gas inlet

Axis of symmetry or center axis

Anode-side, gas outlet to expansion

Temperature

Homogeneous

Constant

Dirichlet

Neumann

User-specified

Thermal Ion Flux

Rec. prob.

Recombination probability

Table 3.3: PLASIMO boundary conditions employed for PW models.

Property
Pressure

Velocity (z)

Velocity (r)

North
H. Neum.

H. Dir.

H. Dir.

West
Cst. Dir. (US)

South
H. Neum. Cst. Neum. (US)

East

Cst. Neum.

H. Neum. H. Neum.

H. Dir.

H. Dir.

H. Neum.

Heavy Temp

Cst. Dir. (US)

Profile Dir. (US) H. Neum. H. Neum.

Electron Temp

H. Neum.

H. Neum.

H. Neum. H. Neum.

Ionization Degree TIF, 90% Rec. prob. H. Neum.

H. Neum. H. Neum.

likely that the deviation from this would not substantially effect model results.

For the 1x6mm 5x10mm and 1x6mm 9x10mm, it is not explicitly known what the outlet

pressure is.

for purposes of obtaining something close to reality, these PLASIMO models

have utilized the anode pressures determined for the corresponding GCS pressure and arc

current of the 1x6mm 7x10mm setup. This introduces a degree of uncertainty, particularly

for the helium case, is it is clear from examining other configurations such as 6x6mm that the

outlet pressure depends more on the total PW length than it does in argon gas. However,

we shall see that other factors render the two-radius PLASIMO models less usable than the

single-radius models.

130

In addition to the boundary conditions in Table 3.5, it is necessary to specify an initial-

izing composition of the plasma bulk region (non-boundary) region of the model.

Another input the user specifies is the current delivered to the system, which is sub-

sequently used in determining the axial electric field strength Ez. PLASIMO takes the

assumption of quasineutrality and as such does not solve Poisson’s equation to determine

electric field (as the net space charge will be zero under this assumption). Instead the axial-

direction electric field is determined using the arc current I and the plasma conductivity

σ(r, z), integrated over the channel area, as:

2π(cid:82) R

I

0 σ(r, z)rdr

Ez =

.

(3.66)

This is the only component of the electric field that is considered in the bulk of the plasma

of the model. This is a good approximation for the part of the arc which has a roughly

homogeneous electric field, which for the plasma window is from about the second plate

(from cathode-side) to the plate just upstream of the anode.
In this homogeneous field
region, as a DC arc, the time derivative of the magnetic field magnitude is 0 so ∇ × E = 0,

and therefore there is no radial component Er of the field [28]. However, from the cathodes

to around the second plate, the measured component voltages indicate the axial field Ez

has not yet reached homogeneity, a fact which appears to be independent of the current and

pressure settings within the scope studied in this work. These facts can be observed in the

next chapter in Figs 4.15 and 4.16.

The plasma conductivity σ(r, z) used in Eq. (3.66) is one of several transport coefficients

solved for in PLASIMO using Frost mixture rules [121] and Chapman-Enskog-Burnett [112]

kinetic theory for transport coefficients, in which the transport coefficients are calculated in

131

terms of Sonine-polynomial expansion coefficients. The other transport coefficients calcu-

lated are electron and heavy particle thermal conductivities, and plasma viscosity. In Section

3.4, the portion of this theory relevant for calculating viscosity was discussed.

For PLASIMO’s viscosity, the first order approximation is used with the electron contri-

bution neglected (as is the case in Section 3.4). For heavy particle thermal conductivity the

third order approximation is used, and the electron-heavy interactions are again neglected.

The electrical conductivity σ is calculated using Devoto’s second order approximation, and

assumes only electrons contribute the conductivity. The calculation of this approximation

is thoroughly detailed in Ref. [122], but in short it relies on contributions from ion and

neutral collisions with electrons, through an ordinary diffusion coefficient calculated using

similar framework described in Section 3.4. Further details on the calculation of the diffu-

sion coefficients is provided in Ref. [112]. For these transport coefficients, it is necessary to

incorporate collision cross section information for neutral-neutral and neutral-ion collisions.

Methodology for obtaining this is given in Ref. [123]. Now this electrical conductivity can

be used in Eq. (3.66) to determine the local axial electric field. This electric field is then

used in determining Ohmic power input QOhm in Eq. (3.61) using:

(cid:90)

QOhm =

j · E dA .

(3.67)

Furthermore, the current density j is determined via Ohm’s Law using:

j(r, z) = σ(r, z)E(z) ,

(3.68)

132

Figure 3.9: Several plasma properties from a PLASIMO model of a 6x6mm PW of argon at
GCS pressure 200 torr and arc current 120 A.

so, coupling with Eq. (3.66):

j(r, z) =

2π(cid:82) R

Iσ(r)
0 σ(r, z)rdr

.

(3.69)

With that, the model is established and can be used to determine plasma properties and

how they compare to measurement. Figure 3.9 shows some results from a converged argon

PLASIMO model in a 6x6mm geometry with a GCS pressure of 200 torr and arc current

of 120 A. As will be discussed in Section 4.2, the electron density ne will be compared to

the corresponding measurement by effectively reconstructing a Stark profile for an emitting

133

Figure 3.10: Similar to Fig. 3.9 but for helium. Several plasma properties from a PLASIMO
model of a 6x6mm PW of helium at GCS pressure 200 torr and arc current 150 A.

plasma with the PLASIMO model’s ne radial profile at the axial position of the diagnostic

plate where measurement occurs. Effectively this means that the model ne value used for

comparison will be close to the on-axis value. The same is true for electron temperature Te.

For plasma conductivity σ to compare with measurement, a radial average is taken over the

model space at the axial location corresponding to the plate in question. A model value of

heavy temperature Th is also determined in this manner and will be compared with the axial

Th profile calculated via the methodology described in Section 3.3.

Generally, features in the argon PLASIMO model roughly match with the measured

134

Figure 3.11: PLASIMO arc current for a 1x6mm 5x10mm model corresponding to a PW
with 200 torr GCS pressure and 120 A arc current. There is a mismatch not only between
the arc current in the two sections but also between both and the experimental arc current.

values, and the same is true for the helium PLASIMO model. Chapter 4 will go into depth

with the comparisons of the various measured properties between the two gases and with

the PLASIMO model.

PLASIMO models of the two-aperture configurations are more complicated than the

single-aperture ones, and exhibited much more difficulty in obtaining a converging solution,

particularly for helium models. The model calculates current density j via Ohm’s law j = σE.

This amounts to using Eq. (3.69) for the single-radius models such as a 6x6mm PW. For the

two-radius system however (e.g. a 1x6mm 5x10mm configuration), the total arc current is

135

0123456100110120130140150160170180 PLASIMO Current Experimental Arc CurrentArc Current [A]Axial Position [cm]not necessarily preserved in going from the smaller radius section of the channel to the larger

radius section, nor are either necessarily equivalent to the corresponding experimental arc

current. This can be seen in Fig. 3.11 for a PLASIMO model of a 1x6mm 5x10mm PW in

argon at 200 torr GCS pressure and 120 A arc current. Essentially, the two-radius model is

intrinsically non-1D, and this particular PLASIMO model is designed for systems that have

a single radius and so can be reasonably well approximated as 1D. This means that utilizing

this type of model to assess the two-radius PW configurations is inappropriate. However,

as will be discussed at length in Section 4.2, the single-radius PLASIMO models perform

reasonably well and generate results that are comparable to measured values.

3.6 Effect of Plasma Window on Ion Beam

The NSCL plasma window test stand is actually just one half of the system that would be

implemented on an accelerator beamline, for ease of experimentation. In an accelerator, there

would be two plasma windows, one on either side of the high pressure GCS. It is necessary

to quantify this system of the plasma windows and gas charge stripper impact on the beam

passing through. The effect of this complete charge stripping apparatus on the beam comes

about in primarily two forms: energy spread and emittance growth from scatterings with

stripping gas particles, and beam-deflection from the magnetic field generated by the arc

current. We will begin with the effect on the beam by the PW arc current I which generates

an azimuthal magnetic field BP W .

In both plasma windows, the electron current flows from the cathodes at the high pressure

side to the anode on the low pressure side. The beam will first traverse one PW (electron

current travelling in the opposite direction as ion beam) with its initial charge state, then

136

Figure 3.12: A diagram illustrating the orientation of an ion beam traversing the PW-GCS
arrangement. Also shown are the magnetic field orientations from the PWs and the resulting
deflection on a beam particle.

will be stripped in the GCS, and finally will traverse a second PW (electron current travelling

in the same direction of the ion beam) which is oriented opposite of the first, with its post-

stripped charge state. In the first PW with the electron current travelling antiparallel to the

beam, the field will deflect beam particles continuously radially inwards, and in the second

PW with the electron current travelling parallel to the beam, the field will deflect beam

particles radially outwards. This is illustrated in the diagram of Fig. 3.12.

Consider a test case of an ion beam traversing a PW that is 8 cm long and carrying 180 A

of arc current. A worst-case scenario would be if all the arc current is constricted and passes

through a narrow radius column within the whole PW channel, and for beam particles just

outside where this arc current travels. For this worst-case example, consider all the current

to be within 1 mm diameter along the PW axis, and a test beam particle right at the edge

of this current, which has initially zero transverse velocity. From Ampere’s Law for particles

outside then:

BP W =

µ0I
2πr

.

(3.70)

137

The Lorentz force dictates the degree of deflection experienced in both cases, so that:

˙vj,⊥ =

cβBP W ±ˆr ,

Qj
mb

(3.71)

where the subscript j denotes which PW the beam is within, mb is the mass of a beam

particle, Q is the charge state of the beam within PW j, β is the beam speed as a fraction of

the speed of light, and ˙vj,⊥ is the deflection acceleration whose direction is given based on

which PW the beam is in (see Fig. 3.12). With this one can obtain the deflection angle and

distance at the end of each PW for the test particle, which are shown in Tab. 3.6. Angular

deflections are moderately sized but changes in the radius of the beam test particle are small

enough that the deflections will not be a concern for beam scraping on the inner surface of

the PW plates. The values in this table can be compared to a test beam, which here will be

the FRIB beam. The FRIB beam at the charge stripper can have a full beam size (radius)

as small as 1.5 - 2.0 mm, with full beam normalized emittance around 1.5 π mm mrad. This

corresponds to an angular extent of about 12.0 - 15.9 mrad. Therefore it can be seen when

comparing to the angular deflection values listed in Tab. 3.6 to these nominal FRIB values,

it is clear that under the assumptions discussed above that the angular deflections generated

by the PW are not negligible. However, we must recall that this is under the assumption

that ALL of the arc current is contained within a 1 mm diameter column along the PW axis.

This is unlikely to be the case, so if we consider instead an arc where the current density

j(r) falls off as 1/r (such that j(r)2πr = constant), we would obtain instead for the PW

magnetic field BP W :

BP W =

µ0I
2πR

,

138

(3.72)

Table 3.4: Characteristics of beam particle deflections from the PW for several test beams
each at 18 MeV/u. Beam particle is initially 1.5 mm from center-axis and has zero angle.

Property
Initial (PW1) Charge State

Outgoing (PW2) Charge State

Gamma

Beta

238U 40Ar
33+
8+

75+

12+

16O
6+

8+

1.019

1.019

1.019

0.193

0.193

0.193

Single PW transit time [ns]

1.4

1.4

PW1 outgoing angle change [mrad]

-0.44

-0.64

PW1 outgoing radius change [µm]

PW2 outgoing angle change [mrad]

PW2 outgoing radius change [µm]

-18

1.0

40

-25

0.96

38

1.4

-1.2

-47

1.6

64

where now the field is constant in r and depends on the PW channel radius R. For a PW

channel of 3 mm radius (6 mm diameter) which corresponds to the geometry discussed at

length in Section 4.2, this results in a BP W that is half of what is used for results in Tab.

3.6 and thus angular deflection values will also be reduced to half the values presented there.

While this latter approach is likely a more realistic scenario, results presented in Tab. 3.6

represent the worst case scenario and therefore worth planning for.

These are the results only for particles matching the specified inlet parameters, but of

course the full beam contains particles over a range of angles and positions. To understand

the effect on the beam as a whole, F. Marti conducted a simulation of a beam packet

consisting of 106 particles whose RMS (un-normalized) emittance is 0.802 pi mm mrad [1].

The effect of the PW is taken as a simple angular kick that would occur at the center of

the PW length, assuming that the current distribution is entirely concentrated in within a

radius of 1 mm. For this calculation, the cumulative current inside this stream increased

quadratically with radius r up to R = 1 mm, so the magnetic field inside this arc current

139

Table 3.5: Beam emittance values resulting from transit through the two PWs enclosing a
GCS (GCS not considered here). RMS emittance results are for a 238U beam with charge
state 33+ for PW1 and 73+ for PW2, and each PW being 10 cm long and 150 A [1].

Location

RMS Emittance Value [pi-mm-mrad]

At PW1 center (before kick)

At PW1 center (after kick)

At PW2 center (before kick)

At PW2 center (after kick)

0.7992

0.8019

0.8019

0.8142

stream is:

,

Bin =

µ0Ir
2πR2

(3.73)

and outside it is given by Eq. (3.70). These two different forms result in nonlinear behavior

for the particles of the entire beam bunch, which is why the beam emittance in this PW case

will increase. The resulting effect on the beam emittance through both PWs is shown in Tab.

3.6. For this test case of a 238U beam in a 180 A pair of PWs, it can be seen that emittance

increases from 0.7992 to 0.8142 pi-mm-mrad, an increase of only 2%. It should also be noted

that this would be the worst-case-scenario with all of the arc current being confined to a

narrow stream in the channel, whereas it’s expected that the arc current is actually spread

over the entirety of the PW channel and therefore the effect on beam emittance would be

further reduced.

The other effect on the beam comes from the gas charge stripper itself. The beam-gas

scattering events within the stripper will result in a net divergence of the beam angle in

all directions, but not appreciable change in beam position coordinates. The result for the

beam’s transverse emittance is qualitatively illustrated in Fig. 3.13 for two scenarios, the

first in which the beam has a smaller extent but greater angle, and vice versa for the second

140

Figure 3.13: Two possible scenarios for beam Courant-Snyder ellipses at the entrance of the
GCS. Beam-gas scatterings will cause angular deflections, growing the ellipse in the x(cid:48), y(cid:48)
directions, and will have a greater overall area growth for Case 2.

scenario. It can be easily visualized then that for the second case, a much greater transverse

emittance growth will occur, so the first case is the desired Courant-Snyder ellipse for the

beam to have at the entrance of the GCS.

As mentioned in Section 1.1, some calculations of of energy spread for a U beam passing

through a 225 torr and 375 torr He charge stripper were carried out in Ref. [3] (shown in

Fig. 1.4). The obvious result of this is that energy spread rises rapidly as a function of the

overall length of the charge stripping region, hence the desire for as short a charge stripper as

possible. The mean charge state asymptotically approaches the equilibrium charge state, so

there must be a user-decided optimization between higher charge states but greater energy

spread (longer stripper) and vice versa (shorter stripper).

141

Chapter 4

Results and Discussion

4.1 Flow Rates in Plasma Window Configurations

It was shown in Fig. 1.6 that the plasma window can substantially reduce the flow rate of the

gas leaking from the GCS. Understanding the degree of this reduction has been a core aim

of this thesis, as is leveraging that understanding to optimize the PW geometry and meet all

the needs of a gas charge stripper for an ion beam. Those necessities are an aperture wide

enough to permit scrape-less beam passage (6 to 10 mm diameter) and as large a pressure

as can be managed to achieve the desired degree of charge stripping in a short length (see

e.g. Fig 1.3). In an effort to better understand how to optimize the PW geometry for those

two factors, an important facet of this project has been the study of different geometries

of the PW, referred to as configurations, and within those the corresponding flow rates for

selected GCS pressure and arc current. The ion beam must pass through the PW without

scraping on the enclosing walls, which is the reason PW aperture sizes of less than 6 mm

are not considered for this application. This requirement encourages more consideration of

a two-radius system such as 1x6mm 7x10mm, where the only 6 mm plate is nearest the

charge stripper. Because the beam experiences angular deflections in the charge stripper,

the beam will grow in extent over the length of the PW, so if the PW has a 6 mm plate in an

otherwise 10 mm channel, it’s best to have that plate on the cathode-side where beam size

142

Figure 4.1: Argon flow (left) and flow reduction factor (right) data taken in multiple PW
configurations, labeled A-G. All data is for a GCS pressure of 200 torr.

will be relatively small. Due to improvements to the PW system being applied after some

data already had been collected for certain PW geometries, and the process of adjusting to a

new configuration being a lengthy one, some PW configurations are lacking data at certain

GCS pressures and/or arc currents.

Figures 4.1 and 4.2 illustrate several key points of the plasma window’s flow rate restrict-

ing capabilities in different plate configurations. In an argon PW, the effect on flow rate of

variations in total channel length for a 6 mm diameter channel is difficult to discern, as seen

with Config. A and Config. B in the figure. In a helium PW though, it does appear that

there is a benefit of reduced flow by extending the PW length. The drawback in extending

143

6075901051201351501651801952100510152025303560759010512013515016518019521002468101214161820ArgonFlow Rate [SLM]Current [A] 6x6mm Plates (Config. A) 8x6mm Plates (B) 3x6mm_3x10mm Plates (C) 1x6mm_5x10mm Plates (D) 1x6mm_7x10mm Plates (E) 1x6mm_9x10mm Plates (F) 6x10mm Plates (G)Flow Reduction FactorCurrent [A]Figure 4.2: Similar to Fig. 4.1 but for helium. Helium flow and flow reduction factor data
taken in multiple PW configurations, labeled A-G as in Fig. 4.1, however due to experimental
limitations no data was acquired for configurations D or G, and data for F was extrapolated
from data at other pressures in that configuration. All data is again for a GCS pressure of
200 torr.

144

60759010512013515016518019521001020304050606075901051201351501651801952100246810121416HeliumFlow Rate [SLM]Current [A] 6x6mm Plates (Config. A) 8x6mm Plates (B) 3x6mm_3x10mm Plates (C) 1x6mm_7x10mm Plates (E) 1x6mm_9x10mm Plates (F)Flow Reduction FactorCurrent [A]the PW length however, as will be shown later in this chapter, is that overall arc voltage

drop increases with the total distance, so there is a greater power being delivered to the arc

that must ultimately be removed by the coolant. The longer distance additionally would

result in more beam size growth. Given that the conductance of a channel is proportional to

its area, it’s no surprise that even with the arc, we see a substantial flow rate rise between a

6 mm diameter channel (Config. A) and one of 10 mm diameter (Config. G) in argon. We

were unable to maintain a stable helium arc in a full 10 mm diameter channel so no Config.

G data was collected for this gas. An additional feature of interest in Figs. 4.1 and 4.2 is

noted by comparing the 3x6mm 3x10mm (Config. C) flow rates with those of 6x6mm (Con-

fig. A) in both gases. As a function of arc current, the slope of the former is much steeper

and appears to approach that of the latter at currents above 90 A in argon. Unfortunately

Config. C is one in which no data was obtained beyond 90 A (this was collected prior to

an upgrade which increased the maximum arc current from 105 A to 210 A), but it is likely

that at currents higher than about 100 A, the flow rate in this system will be essentially the

same as in the case of Config. A. This suggests that, for currents in excess of this, there is

very little benefit in a PW longer than 3 plates (recall the plates are 7 mm wide with 2 mm

wide spacers). Such behaviors presumably also would be illustrated for e.g. a PW consisting

of 2 plates, etc.

All of the measurements of plasma properties have been taken with the aim of determining

how they depend upon the plasma window’s controllable parameters - its pressure, current,

and geometry. It is necessary to establish predictable behaviors of these properties because

these in turn influence the mass flow through that same channel. The subsequent sections in

this chapter are devoted to illustrating results of these measurements and their significance,

beginning with single-radius PW configurations in Section 4.2, which primarily emphasises

145

the 6x6mm PW configuration (Config. A) and then for double-radius PW configurations

such as 1x6mm 7x10mm in Section 4.3, which will detail a smaller subset of results.

4.2 Single-Aperture Plasma Window Results

In this and the subsequent section, results from both gases will be introduced. Those in

this section are from PW arrangements consisting of a single aperture size that extends the

length of the channel.

As mentioned in Section 1.1, a gas charge stripper composed of helium produces the

highest charge states in the transiting ion beam relative to other gas options (with the

exception of hydrogen), but as a result of its low mass, also has a high leakage rate from

the GCS. In addition, while the argon arc is quite stable and can be maintained through a

very wide range of operating conditions, the helium arc is more difficult to manage. In order

to even establish a stable arc in helium, we have found it necessary to initiate the arc in

argon, and then slowly close the argon flow and simultaneously open that of helium. This is

thought to be a result of helium’s lower mass not being able to sufficiently heat the cathodes

from a null current state to allow them to emit electrons enough to establish a stable arc.

One thing that contributes to this difficulty of helium in the PW is that it has a rather high

first ionization energy of 24.59 eV, as compared to argon’s first ionization energy of 15.76

eV, as well as having lower ionization cross section values. As a result, helium requires a

higher electron temperature to generate the same density of ions in the plasma.

146

4.2.1 PLASIMO Comparison Method

It should be noted that for electron density measurements, proper comparisons with PLASIMO

require some assumptions. Firstly, at any axial location we naturally expect a radial dis-

tribution in electron and heavy particle densities and temperatures and so too would we

expect a radial distribution of the intensities of emission lines. Some previous works indicate

that the electron density tends to fall to about 1/10 of its central value near the edge of the

arc channel of its central value [81]. We therefore expect a dramatic reduction in emission

intensity distribution closer to the edge of the arc channel. We will denote this intensity

distribution by e(r). Additionally, since measurements take in light along the entire line of

sight which cuts through the central chord of the arc channel, in order to properly compare

PLASIMO model to measurement the modeled values should be a mean value over a re-

gion corresponding to the measurement and weighted by the emission intensity distribution

mentioned above.

Firstly we will make a simple estimate of what the intensity distribution e(r) would

be. Measurements of this distribution in a cascaded arc setup similar to the PW has not

been thoroughly examined or published, as of the time of this thesis, though it would be

a very interesting arc characteristic to be explored. Lacking measurements, we can model

an expected e(r) using the HeCRM discussed in Section 3.2 using PLASIMO modeled ng

and ne for a test case. The test case corresponds to data from P2/6 of a 6x6mm PW at

GCS pressure 200 torr and arc current 150 A, and the results are illustrated in Fig. 4.3. An

exponential decay is fitted, which will be taken as the intensity distribution e(r) that will be

used in the rest of the analysis in the subsequent paragraphs.

We must consider the volume of the arc channel whose emissions will transmit through

147

Figure 4.3: Simulated relative radial intensities for three selected emissions for a 6x6mm
PW, using PLASIMO modeled data corresponding to P2/6, GCS pressure 200 torr, and arc
current 150 A. The dashed line is an exponential decay fit, representing the radial intensity
distribution e(r) to be used.

148

0.00.20.40.60.81.00.00.10.20.30.40.50.60.70.80.91.0 388.9 nm emission 447.1 nm emission 492.1 nm emissionRelative Emission Intensity (I(x) / I(0))Relative Radial Position (x = r / R)the 1 mm diameter diagnostic port at the side of the channel. We assume all light that enters

the port is collected by the receiver, and from this point forward all emissions mentioned are

implied to be parallel to the diagnostic port. Consider such a port whose diameter is b, on

the outside of the arc channel of radius R. Considering a succession of concentric, differen-

tial thickness cylinders that are coaxial with the arc channel, we must find the volumetric

intersection of this cylindrical shell and the diagnostic port line of sight (LOS) cylindrical

column. A far easier problem can be constructed if we consider that the diagnostic port

LOS is instead a square column, each side being b wide. With this, it can be shown that for

the cylindrical shells of r < b/2, the intersection volume (between that shell and the LOS

column) is:

For cylindrical shells of r ≥ b/2, only part of the shell intersects the LOS column, so:

dV = b

2πr

(cid:17)(cid:33)(cid:35)
dr = 4br sin−1(cid:16)2r

(cid:17)

dr .

b

dV = 2πbrdr .

(cid:34)

(cid:32)

(cid:16)2r

b

2
π

arcsin

(4.1)

(4.2)

Given that each of these radii r corresponds to a different electron density ne(r), emissions

from these shell-LOS intersections will each have a different profile whose shape is given by

Eq. (2.15). For this analysis, it is necessary to use the width wj, shift d, and asymmetry

parameter α that parameterize the Stark profile corresponding to the radially-dependent

electron density ne(r). To reconstruct a PLASIMO value for electron density which can

be compared to measurement, a reconstructed Stark profile is sought, by considering the

emission profile at each radius r. At each r, the emission profile must be normalized according

to both the differential emission volume in Eqs. (4.1) and (4.2), and the emitter density given

149

Figure 4.4: Normalization factors for reconstructing a would-be-observed Stark profile from
PLASIMO measurements. The black solid line is the geometric normalization using Eqs
(4.1) and (4.2), the red dotted line is the emission normalization factor from Fig. 4.3, and
the blue dash-dotted line is the (renormalized) product of the other two curves. The green
dash-dot-dot line is the cumulative integration of the blue overall factor.

by e(r), explained in Fig. 4.3. These normalizations are obtained by setting the greatest
value over the domain 0 ≤ r ≤ R equal to 1. These normalization values are shown in

Fig. 4.4 for a 6 mm diameter PW channel. An overall normalization factor is obtained

by multiplying the geometric and emission normalization factors (again the greatest value is

reset to 1). The curve in green is the cumulative integration of the blue overall normalization

factor, and this then represents the fraction of total collected emissions that originate within

a given radius.

150

0.00.51.01.52.02.53.00.00.20.40.60.81.0Normalization FactorRadius [mm] Geometric Factor Emission Factor Overall Normalization Factor Cumulative Overall FactorFigure 4.5: Stark profiles at selected radii, using overall normalization factors from Fig.
4.4. The profiles are constructed using Stark parameters corresponding to radial electron
densities determined by PLASIMO for an argon 6x6mm PW, GCS at 200 torr and 120 A,
at the axial location corresponding to P6/6.

To illustrate the behavior of the profiles as their parameters change with ne(r), a set of

reconstructed Stark profiles at selected radii from a PLASIMO model of an argon 6x6mm

PW, GCS at 200 torr and 120 A, (at the equivalent position of P6/6) is illustrated in Fig.

4.5. Each profile’s irradiance integral is given by the corresponding total normalization factor

from Fig. 4.4.

The final thing to consider before reconstructing a Stark profile and obtaining from

it an effective electron density to compare with measurement, is to examine the effect of

151

-0.2-0.10.00.10.20.30.00.51.01.52.02.53.03.54.04.55.05.5Irradiance [a.u.]Wavelength [nm] r = 0.411 mm r = 0.865 mm r = 1.14 mm r = 1.40 mm r = 1.64 mm r = 1.86 mmreabsorption of the emitted radiation over the extent of the profile. This reabsorption can

occur anywhere between the emission point and the light collection point. This is included

via Eqs. (2.32) - (2.36). Determining the effect of reabsorption relies on knowledge of the

absorbing state density. This can be obtained via a CR model, such as that described in

Section 3.2. For the arc conditions studied in the PW work for this thesis, the absorbing

densities nabs for emissions studied are typically lower than the ground state density by 6-7

orders of magnitude, based on the CR model results. Even taking the far more generous

value of nabs ≈ 10−4ngrd, the effect of reabsorption on distorting the overall reconstructed

Stark profile appears negligible for the lines studied here (Ar I 425.9 nm and He I 447.1 nm).

A sample of the effect on the overall reconstructed profile is shown for these emission lines

in Fig. 4.6 for both nabs ≈ 10−4ngrd and nabs ≈ 10−3ngrd. For the latter, it is clear that

there starts to be some noticeable impact, though this is a far higher absorber density than

expected. For the argon emission though, even the larger absorber density value doesn’t

result in any appreciable change in the profile shape.

The reconstructed profile S(λ) itself can be expressed as:

(cid:90) R

0

S(λ) =

jA=1(r, λ)NG,e(r)dr .

(4.3)

In this equation, Stark profiles at individual radii are given by jA=1(r, λ), with the subscript

A = 1 simply to note that the area under the profile is normalized to 1. The overall

normalization factor is given by NG,e(r), with the subscripts to declare that it includes both

geometric and emission normalization factors. Explicitly then, this normalization factor is

152

Figure 4.6: Reconstructed Stark profiles without any reabsorption as well as with, at two
different absorber densities. This is for a 6x6mm PW, GCS at 200 torr and 120 A for both
gases, at the axial location corresponding to P6/6.

given by:

NG,e(r) = CdV (r)e(r) ,

(4.4)

where C is chosen such that the greatest value of NG,e(r) = 1. Now with the use of Eq. (4.3)

we can obtain a reconstructed Stark profile from the entirety of PLASIMO’s radial values

of electron density, which we can then perform a Stark-profile fit to and obtain an effective

electron density. At last, this electron density we obtain from the fit of a total reconstruction

of an emission profile is the electron density that can be compared with measurement. For

153

-0.2-0.10.00.10.20.3024681012-0.3-0.2-0.10.00.10.20.30.401234567Reconstructed Irradiance [a.u.]Wavelength [nm] No reabsorption   ,  wJfit =  0.0587 nm nabs(r) = 10-4ng(r)  ,  wJfit = 0.0587 nm nabs(r) = 10-3ng(r)  ,  wJfit = 0.0587 nmAr I 425.9 nmHe I 447.1 nmWavelength [nm] No reabsorption   ,  wJfit =  0.0577 nm nabs(r) = 10-4ng(r)  ,  wJfit = 0.0581 nm nabs(r) = 10-3ng(r)  ,  wJfit = 0.0577 nmFigure 4.7:
Left: The overall reconstructed profile and corresponding Stark fit using
PLASIMO radial electron densities for an argon 6x6mm PW, GCS at 200 torr and 120
A, at the axial location corresponding to P6/6. Right: Comparison of various Stark widths.
Black points are PLASIMO modeled values at radial values inside arc channel. The green
solid line represents the Stark width measured during PW operation, and the orange dot-
dashed line represents the Stark width of the fit to the PLASIMO overall reconstructed
profile.

the same test case as above, an argon 6x6mm PW, GCS at 200 torr and 120 A, at the axial

location corresponding to P6/6, the results are shown in Fig. 4.7.

This figure illustrates PLASIMO’s modeled Stark width wj as a function of radius r, as well

as wj determined from the fit to the overall reconstructed Stark profile, and the physically

measured wj value for the same operating condition of 200 torr and 120 A. These latter

two are denoted in the figure as lines but it should be mentioned that the interpretation is

154

-0.4-0.3-0.2-0.10.00.10.20.30.40123456789100.00.51.01.52.02.53.00.000.010.020.030.040.050.060.07Irradiance [a.u.]Wavelength [nm] Reconstruction Stark Fit Stark width of PLASIMO at radii Measured Stark width Stark width of reconstructed profileStark Width [nm]Radial Position [mm]simply that it’s the value corresponding to the entire line of sight and does NOT mean these

are values that are constant across the arc channel’s radius. Analogous results for helium

6x6mm PW, GCS at 200 torr and 120 A, at the axial location corresponding to P6/6 are

shown in Fig. 4.8.

Figure 4.8:
Left: The overall reconstructed profile and corresponding Stark fit using
PLASIMO radial electron densities for a helium 6x6mm PW, GCS at 200 torr and 120
A, at the axial location corresponding to P6/6. Right: Comparison of various Stark widths.
Black points are PLASIMO modeled values at radial values inside arc channel. The green
solid line represents the Stark width measured during PW operation, and the orange dot-
dashed line represents the Stark width of the fit to the PLASIMO overall reconstructed
profile.

155

-0.4-0.20.00.20.40.601234560.00.51.01.52.02.53.00.000.010.020.030.040.050.060.07Irradiance [a.u.]Wavelength [nm] Reconstruction Stark Fit Stark width of PLASIMO at radii Stark width of reconstructed profile Measured Stark widthStark Width [nm]Radial Position [mm]Figure 4.9: Electron densities in argon arc at two axial locations along the 6x6mm PW
channel. The data set at left is taken at plate 2/6 and the data set at right is at plate 6/6.
Comparisons with corresponding PLASIMO model electron densities at those axial locations
are shown also obtained by a Stark fit to an overall reconstructed Stark profile.

4.2.2 Electron Density

Certain electron density trend behaviors are expected. We expect that increasing arc current

will produce an increase in electron density due to a greater amount of electrons being ex-

pelled from the cathodes. As these electrons each contribute to ionization of the background

gas particles, this increased electron density from the cathodes propagates down the entire

length of the channel. Increasing GCS pressure would also contribute an increase in electron

density, as the collision rate of the electrons and neutrals-to-be-ionized increases as a result

156

60901201501802100.00.51.01.52.02.53.03.54.04.55.05.56.06.560901201501802100.00.51.01.52.02.53.03.54.04.55.05.56.06.5Plate 6/6Electron Density [1016 cm-3 ]Current [A] 200 torr ( PLASIMO) 300 torr ( PLASIMO) 400 torr ( PLASIMO)Plate 2/6Electron Density [1016 cm-3 ]Current [A]Figure 4.10: Similar to Fig. 4.9 but for helium. Electron densities in helium arc at two
axial locations along the 6x6mm PW channel. The data set at left is taken at plate 2/6 and
the data set at right is at plate 6/6. PLASIMO comparison data also shown.

of increased presence of neutrals, the ionization rate which is proportional to the neutral

density is increased. Electron density as determined by Stark broadening (see Section 2.2.2)

is calculated at diagnostic plate locations along the plasma window’s length, as discussed in

Section 2.1. Results of these calculations at two such locations - P2/6 and P6/6 - in a 6x6mm

PW are shown in Fig. 4.9 for argon arc and Fig. 4.10 for helium arc. Since the electrons

are the particles which are primarily responsible for heating the gas, the electron density

dictates the rate of this heating. Additionally, the electron density is used in determining

ionization degree as in Eq (3.19), as well as the mass flow relationship, described in Section

157

75901051201351501651800.100.150.200.250.300.350.4075901051201351501651800.100.150.200.250.300.350.40Plate 6/6Electron Density [1016 cm-3 ]Current [A] 150 torr ( PLASIMO) 200 torr ( PLASIMO) 300 torr ( PLASIMO)Plate 2/6Electron Density [1016 cm-3 ]Current [A]Figure 4.11: Electron density in argon PW for two different configurations, a 6x6mm (left)
and 6x10mm (right). In both cases the electron densities are for P6/6.

3.3.

It is evident that the predicted behaviors mentioned in the preceding paragraph are

borne out in the empirical results of Figs. 4.9 and 4.10, though ne in the helium arc seems

to have less dependence on the arc settings than in the case of argon. Furthermore, as

a result of having both a higher ionization energy and lower ionization cross section (from

ground state), helium’s electron densities are generally about an order of magnitude less than

those in argon. They additionally appear to have less variability with changing operating

conditions. Additionally, in Fig. 4.11, a comparison is provided for ne measurements in

158

60901201501802100.00.51.01.52.02.53.03.54.04.55.060901201501802100.00.10.20.30.40.50.60.70.80.91.01.11.21.3Electron Density [1016 cm-3 ]Current [A] 100 torr 150 torr 200 torr 250 torr 300 torr 350 torr 400 torr6x6mm6x10mmCurrent [A]argon at P6/6 for a 6x6mm PW and a 6x10mm PW. Noting the difference in scales, the

electron density ne is vastly decreased in the larger-diameter channel. This is likely the

reason why the helium arc was unable to be established with any semblance of stability for

this 10 mm diameter channel geometry as mentioned in Section 4.1, assuming that it too

would have a significantly lower electron density than the case of 6 mm diameter channel.

4.2.3 Electron Temperature

Electron temperature Te is another essential plasma characteristic necessary to determine,

and impacts calculations of numerous other plasma properties. As with any temperature,

the electron temperature characterizes the kinetic energies associated a certain distribution

of electrons, and strictly speaking the manner this electon temperature is employed in this

work is valid only for Maxwellian EEDFs. It is for that reason necessary to know, or at least

make realistic inferences about, the shape of the EEDF. In plasmas of sufficient density, the

EEDF assumes a Maxwellian distribution because the electron-electron collision frequency

which acts to redistribute energy is much greater than the frequency of inelastic collisions

with the heavies which otherwise deplete the high energy electrons and cause a drop off of

the tail of the EEDF. A more thorough discussion to determine the extent of this effect is

presented in Section 3.1, the result being that it’s very likely the EEDF is well-approximated

by a Maxwellian shape.

The procedure used to determine electron temperature in argon is the creation of a

Boltzmann line from spectroscopically collected relative emission intensities (see Section

2.2.3), whereas for helium, the relative emission intensities must be compared with results

of a collisional-radiative model (see Section 3.2). As mentioned previously, the emissions

observed at diagnostic plate locations are taken over a central chord of the channel’s cross

159

sectional area. Similar to the case of calculating ne, it is assumed that the calculated Te is

the central, on-axis value due to most of the emitted photons originating from the innermost

1 mm of the arc as seen in Fig. 4.4.

Measured electron temperature for argon in a 6x6mm PW are presented in Fig 4.12, at

locations P2/6 and P6/6. These results suggest that between these locations, the electron

temperature through the discharge channel doesn’t appear to change drastically, but gen-

erally does show a gradual increase from the cathode to anode side. Additionally, electron

temperatures in lower pressure environments tend to be greater than those in higher pres-

sures. This net result of a slight increase in electron temperature with distance down the

channel is also seen in PLASIMO model results, as well as previous publications [41, 117].

The Boltzmann plot method is again applied for helium arc using emission lines indicated

in Table 2.4. However, as explained in Section 2.2.3, this time the temperature obtained as

the excitation temperature Texc is unlikely to be equatable to the electron temperature Te.

The excitation temperatures are generally too small to really correspond to the electron

temperature, being in the area of 0.5 eV. It is expected that the electron temperature is

significantly higher than this, which motivates the need to utilize an additional tool, a

collisional-radiative model. The model used in this work (HeCRM), originally crafted by

T. Fujimoto [15] and later revisited and updated by M. Goto [14], as discussed in Section

3.2. Also in that section, the process for obtaining a synthetic spectra using the HeCRM

is outlined, and relies on determining which set of measured emissions is close enough in

their relative intensities to the set of synthethesized emissions, which are generated at a

series of test electron temperatures Tt, selecting that temperature which best reproduces

the measured relative intensities as the electron temperature Te. Results of both excitation

temperature Texc from Boltzmann plot method and Te determined using the HeCRM are

160

Figure 4.12: Electron temperature at plate 2/6 and plate 6/6 as determined by Boltzmann
line method with Ar II lines in a 6x6mm argon PW. Dotted lines and open points show the
result from PLASIMO model corresponding operating conditions. The model values have
been integrated over the channel radius at the relevant axial location.

161

60901201501802101.01.11.21.31.41.51.61.71.81.92.02.160901201501802101.01.11.21.31.41.51.61.71.81.92.02.1Plate 6/6Electron Temperature [eV]Current [A] 200 torr ( PLASIMO) 300 torr ( PLASIMO) 400 torr ( PLASIMO)Plate 2/6Electron Temperature [eV]Current [A]Figure 4.13: Measured excitation temperature Texc from Boltzmann line method (left), and
electron temperature Te from comparison of measured relative intensities to those calculated
using HeCRM. The top two plots pertain to plate 2/6 and the bottom two pertain to plate
6/6. Note the difference in scales of the y-axes.

shown in Fig. 4.13. As with Fig. 4.12 for argon, these helium results pertain to a 6x6mm

PW at diagnostic plate locations of P2/6 and P6/6. An interesting feature here is that it

appears that excitation temperature Texc largely behaves oppositely than does the electron

temperature Te, with respect to GCS pressure and arc current.

These same electron temperature Te results are also shown in Fig. 4.14 along with

the corresponding PLASIMO modeled values. Here it is clear that the trends mentioned

regarding Te in argon from Fig. 4.12 are also evident here: Te increases at higher arc

162

75901051201351501651801.822.22.42.62.8375901051201351501651800.250.30.350.40.450.50.5575901051201351501651800.40.50.60.70.80.911.175901051201351501651801.51.61.71.81.922.12.22.32.4Plate 6Electron Temperature [eV]Current [A]Plate 6Excitation Temperature [eV]Current [A] 150 torr 200 torr 250 torr 300 torrExcitation Temperature [eV]Current [A]Plate 2Plate 2Electron Temperature [eV]Current [A]currents and decreases at higher GCS pressures, and Te increases somewhat between P2/6

and P6/6.

Figure 4.14: Electron temperature at plate 2/6 and plate 6/6 as determined by Boltzmann
line method with He I lines in a 6x6mm helium PW. The collisional-radiative model [14, 15]
in conjunction with measured electron densities from Fig. 4.10 to determine these electron
temperatures. Dotted lines and open points show the result from PLASIMO model cor-
responding operating conditions. The model values have been integrated over the channel
radius at the relevant axial location.

4.2.4 Electric Field and DC Conductivity

Another plasma property that plays an essential role in influencing the dynamics is the axial

electric field, which is related to the electron energy gain and therefore the degree of heating

163

75901051201351501651801.61.82.02.22.42.62.83.075901051201351501651801.61.82.02.22.42.62.83.0Plate 6/6Electron Temperature [eV]Current [A] 150 torr ( PLASIMO) 200 torr ( PLASIMO) 300 torr ( PLASIMO)Plate 2/6Electron Temperature [eV]Current [A]Figure 4.15: Electric field in argon 6x6mm PW with GCS pressure 200 torr, calculated from
floating plate voltages. The inset is the derivative of this electric field with respect to axial
position.

and ionization for the heavies. In Section 2.1.3.3, it was explained how the axial electric field

E is obtained using the floating voltages of the metal plates enclosing the plasma. Note that

the field is calculated from the difference of voltage between plates, so axial values for the

field are set as the midpoint between the plates. This field provides a means of continually

replenishing electron energy following inelastic collisions with the heavy particles, which

deplete the electron kinetic energy. Figure 4.15 shows these electric field measurements in a

6x6mm configuration in argon of GCS pressure 200 torr as a function of the axial position,

given here as a fraction of the total PW length, and Fig. 4.16 shows the electric field with the

same conditions except in helium. In both gases the central region of the PW (corresponding

to fractional position of about 0.4 to 0.85 in the figure), with starting point is defined as

between plates 2 and 3, and ending point defined as between penultimate and ultimate pre-

anode plates, conveys an electric field that is relatively constant over the region. This inner

164

Inset 60 A 75 A 90 A 105 A 120 A 150 A 180 A 210 A6090120150180210-240-200-160-120-80-400dE/dz [kV/m2]Current [A]Figure 4.16: Similar to Fig. 4.15 but for helium. Electric field in helium 6x6mm PW with
GCS pressure 200 torr, calculated from floating plate voltages. The inset is the derivative of
this electric field with respect to axial position.

region, whose field is denoted as Ein, is shown in Fig. 4.17 for both gases as a function of

both GCS pressure and arc current in a 6x6mm PW. As is clearly seen in this figure, helium’s

central electric field behavior as a function of current is different than that of argon. In the

argon arc, increasing current results in an increasing Ein. In the helium arc however, this

central region electric field is relatively unchanged with increases in current.

The axial behavior of the PW electric field is qualitatively very similar to that described

in Chapter 10 of Ref. [28], including near the cathodes and anode. As seen in Figs. 4.15

and 4.16, a sharp increase in field strength is measured between the anode and the plate

immediately adjacent to it. Ref. [28] outlines two possible contributions to this anode fall:

one from the negative space charge in the near vicinity of the anode since ions are repelled

towards the cathode, and another related to the contraction of the positive column’s cross

sectional area to the surface area exposed of the anode (this effect is notable if the latter is

165

Inset 72 A 90 A 105 A 120 A 150 A 165 A 180 A6090120150180-320-280-240-200-160-120-80-400dE/dz [kV/m2]Current [A]less than the former).

Inner electric field strengths Ein for arcs in 6x6mm PW at various GCS
Figure 4.17:
pressures and arc currents. The region’s starting point is defined as between plates 2 and 3,
and the ending point is defined as between penultimate and final pre-anode plate.

A sharp drop in electric field magnitude is also observed on the cathode side resulting

from the cathode sheath layer formed in the cathode’s nearest vicinity. This sheath is

characterized by an enhanced density of positive ions which are attracted to the cathode

surface’s accumulation of negative charges that form the surface potential barrier [28, 124].

A striking feature of this side can be seen in the inset of these figures where the axial

derivative of the electric field is plotted for the region circled in the primary figure. The field

drops greatly from cathodes to the first plate (nomenclature is Cath-P1) for lower currents,

166

60901201501802100.00.20.40.60.81.01.21.41.61.860901201501802100.00.20.40.60.81.01.21.41.61.8Inner PW Electric Field [V/mm]Current [A] 150 torr 200 torr 250 torr 300 torr 350 torr 400 torrArgonHeliumCurrent [A]Figure 4.18: Electrical conductivity of the arc for several currents in a 6x6mm argon PW
with GCS pressure at 200 torr. PLASIMO model results are shown as well. The model
values have been integrated over the channel radius at the relevant axial location.

but exhibits shallower field drops at higher currents.

This electric field can be used to determine a mean plasma conductivity over the channel

all the way down its length by assuming a uniform current distribution via Eq. (3.33).

This is shown in Fig. 4.18 for a 6x6mm PW in argon, GCS pressure at 200 torr, and Fig. 4.19

for a 6x6mm PW in helium, also with GCS pressure at 200 torr. Also shown is PLASIMO

modeled conductivity averaged over the channel area, which generally reproduces measured

behavior and magnitude in the central region, though there are deviations at the cathode

and anode regions, as a result of PLASIMO not being able to treat sheath effects [111, 120].

167

0102030405060012345678Plasma Conductivity [kS/m]Axial Position [mm] 90 A ( PLASIMO) 120 A () 150 A () 180 A () 210 A ()Figure 4.19: Similar to Fig. 4.18 but for helium. Electrical conductivity of the arc for
several currents in a 6x6mm helium PW with GCS pressure at 200 torr. PLASIMO model
results are shown as well. The model values have been integrated over the channel radius at
the relevant axial location.

One distinction to note here is that the measured conductivity is obtained by assuming a

uniform current distribution, whereas PLASIMO does not make this assumption and allows

the current distribution to vary over the channel’s cross sectional area.

It is worth pointing out that there is a degree of inherent uncertainty in the locations of

calculated electric field and so plasma conductivity due to the width of the plates. From the

plate structure described in Section 2.1, the metal plates are 7 mm wide and separated by 2

mm thick insulating spacers. As mentioned above, electric fields calculated from differences

168

0102030405060012345Plasma Conductivity [kS/m]Axial Position [mm] 90 A ( PLASIMO) 120 A () 150 A () 180 A ()Figure 4.20: Power removed by water coolant for each PW plate in a 6x6mm configuration
in argon arc. Each data set is taken at a GCS pressure of 200 torr.

in plate voltages are assumed to be the value at the midpoint between the plates (so 9

mm separations), and the electric field between cathodes and plate 1 is calculated using the

distance from cathode tip to the midpoint of plate 1 (about 7.5 mm). Error bars shown in

Figs. 4.18 and 4.19 are determined from a location measurement uncertainty of 0.5 mm and

voltage measurement uncertainty of 0.05 V.

169

0102030405060020406080100120140160180200220 90 A ( PLASIMO) 120 A () 150 A () 180 A () 210 A ()Heat Deposition per length [kW/m]Axial Position [mm]4.2.5 Component Heat Depositions

Another characteristic of the PW that is necessary to examine is the heat deposited by the

arc into the cooled housing components. Not only will the results presented in this section

hopefully assist future endeavors with cascaded arcs in adequately preparing for the heat

load imposed by the arc, but they are also necessary to include phenomenologically in the

1D analysis model described in Section 3.3 for the term related to heat conduction. Since

the PW is operated in a steady state condition, an equilibrium is established between the

heat power from plasma to wall and the power from wall to water and is given as Hw. As

described in Section 2.1.3.2, Hw is determined via calorimetric analysis of the water coolant.

For each plate it is assumed that the power deposited per unit length is constant over the

plate’s plasma-facing wall.

The power deposited into the PW plates, Hw, is shown in Fig. 4.20 for an argon arc in

a 6x6mm PW with GCS pressure at 200 torr. The corresponding plot for the helium arc of

the same operating conditions is in Fig. 4.21. This makes evident an additional challenge of

maintaining the helium arc as opposed to the argon one: the strain on the cooling system

is considerably greater for helium of comparable operating conditions.

It can be seen in

both gases that there is a gradual increase in the power deposited to the plates from the

cathode-side ones, moderately leveling off for the plates closer to the anode.

There is a feature of inconsistency in plate heating measurements of the diagnostic plates,

which is illustrated in Fig. 4.22 An assumption for calculating the plate heat deposition is

that each component connected to the same coolant manifold receives approximately the

same flow rate. As explained in Section 2.1.3.2, the coolant flow rate for the entire manifold

is measured. As a result, one potential reason for the behavior illustrated in Fig. 4.22 is

170

Figure 4.21: Similar to Fig. 4.20 but for helium. Power removed by water coolant for each
PW plate in a 6x6mm configuration in helium arc. Each data set is taken at a GCS pressure
of 200 torr.

171

01020304050600306090120150180210240270300 90 A ( PLASIMO) 120 A () 150 A () 180 A ()Heat Deposition per length [kW/m]Axial Position [mm]Figure 4.22: Shown are data from two separate collections from a 6x6mm PW in helium
gas, one which had a single diagnostic plate at plate 2, and one which had a single diagnostic
plate at plate 6. For both, GCS pressure was 200 torr and arc current was 120 A. At left is
the power deposited to the plates determined by calorimetry and at right are voltage drops
between adjacent plates. Circled regions highlight where behavioral differences between the
two collections would be expected due to the diagnostic plate’s presence or lack thereof.

172

1234560.50.60.70.80.91.01.11.21.3P1-P2P2-P3P3-P4P4-P5P5-P6P6-An10121416182022Power Deposited [kW]Plate Number Plate 2 = diagnostic plate Plate 6 = diagnostic plateVoltage Drop [V]He 6x6mm200 torr 120 Athat the non-diagnostic plates and the diagnostic plates may actually be receiving unequal

coolant flows from the manifold.

For this particular PW system studied in this thesis, it became evident that for some

operating conditions with the 8x6mm configuration, the power deposited into the anode-side

plates was too great to be sufficiently cooled, and vacuum sealing failed each attempt. A

system in which there is a greater number of cascaded plates could help alleviate this. There

would not be a considerable change in power delivered to the arc and therefore to the wall

as a whole, but with a greater quantity of plates, each one will sustain a lesser heat load.

4.2.6 Contributions to Flow Rate Reduction

As stated in the Abstract of this document, one of the principal goals of this work was to

understand with greater clarity and quantitative support what specifically about the arc

contributes to the flow rate reduction that it generates (see Figs. 4.1 and 4.2 for the flow

reduction). As mentioned in Section 1.1, there have been suggested multiple mechanisms

for the flow reduction, primarily the feature of the arc having a higher viscosity than that of

the ordinary room-temperature-gas counterpart [35]. We will examine this claim by looking

at the relative contribution of viscosity directly to the mass flow, where it appears in Eq.

(3.26) as G, as well as indirectly by considering the effect of viscous heating of the plasma,

given by the term Qv (defined in Eq. (3.40)) described in Section 3.3. This effect of viscous

(cid:115)

heating impacts the evolution of the heavy temperature Th which then influences the term

in the mass flow equation Eq. (3.26).

n2
n(cid:48)
h
h
As we see in Figs. 4.23 and 4.24, which show PLASIMO-modeled viscosity values aver-

aged over 3/4 of the channel radius, the presence of the arc does indeed result in a greater

viscosity than that of a room temperature gas. However, the expression obtained in Section

173

Figure 4.23: PLASIMO viscosity values for argon 6x6mm PW at axial points along arc
channel. The viscosities were obtained by averaging over the inner 3/4 of the full channel
radius. Left: GCS pressure at 200 torr and various currents. Right: GCS pressure at 150 A
and various GCS pressures. The room temperature gas viscosity of argon is about 2.2 × 10−5
Pa*s.

3.3.1 for mass flow, Eq. (3.26), suggests that the significance of this viscosity for the mass

flow depends upon the relative quantities of the viscous term G and the total plasma pres-
sure drop term −P(cid:48)

p (the negative sign is included to make the term positive since P(cid:48)

p itself

is negative).

In Figs. 4.25 and 4.26, ratios

−P(cid:48)
G of these two contributions to the mass flow are shown

p

for a variety of PW conditions, using values obtained from PLASIMO models. From these,

it is clear that for all conditions and at all axial points, the viscous term G is at most 20%

of the pressure drop term.

It is thus clear that viscosity doesn’t play a direct role in the mass flow. As a result,

174

010203040500.000000.000050.000100.000150.000200.000250.00030010203040500.000000.000050.000100.000150.000200.000250.00030Viscosity [Pa*s]Axial Position [mm] 200 torr 60 A 200 torr 90 A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 200 torr 150 A 300 torr 150 A 400 torr 150 AFigure 4.24: Similar to Fig. 4.23 but for helium. The room temperature gas viscosity of
helium is about 2.0 × 10−5 Pa*s.

there are dominantly two factors which effect the flow rate: a density factor

and the

(cid:113)−P(cid:48)

pressure drop factor
positive, since P(cid:48)

p and n(cid:48)

p where the negative sign is included to make the overall factors

h themselves are negative. The behavior of the former, the density

(cid:115)
− n2
n(cid:48)

h

h

(cid:113)−P(cid:48)

factor, is illustrated in Figs. 4.27 and 4.28 for argon and helium respectively. Greater

values of this density factor result in greater mass flows. We can compare the behavior

of this density factor with that of the aforementioned pressure drop factor

p, which

is illustrated in Figs. 4.29 and 4.30. It is noted that, with a constant GCS pressure and

varying arc currents, the pressure drop factor does not change significantly, contrary to the

density factor which does change substantially. For a constant pressure, the heavy particle

density nh (see Eq. (3.18)) decreases as heavy temperature Th, electron density ne, and

electron temperature Te increase, and all three of these properties tend to increase with

175

010203040500.000000.000050.000100.000150.000200.000250.00030010203040500.000000.000050.000100.000150.000200.000250.00030Viscosity [Pa*s]Axial Position [mm] 200 torr 90A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 150 torr 150 A 200 torr 150 A 300 torr 150 AFigure 4.25: PLASIMO ionization degree values for argon 6x6mm PW at axial points along
arc channel. These were obtained by averaging over the inner 3/4 of the full channel radius.
Left: GCS pressure at 200 torr and various currents. Right: GCS pressure at 150 A and
various GCS pressures.

arc current. Furthermore, the rate at which the heavy particle density changes down the
channel, given by n(cid:48)

h, also increases with increasing arc current. Therefore it is concluded

that it is primarily this density factor

in the PW.

h

which contributes to the mass flow reduction

(cid:115)
− n2
n(cid:48)

h

(cid:115)

n2
n(cid:48)
h

h

explained

Though it was previously established that viscosity does not appreciably impact the mass

flow in a direct manner, it can still indirectly influence the density factor

above. As suggested earlier, to complete the conclusion that viscous effects are not playing

a substantial role in the mass flow, we must look at the relative impact of viscous heating

relative to other heating mechanisms. The mechanism which heats the heavy particles in

the plasma are collisions with electrons, so we can compare this heating term defined by Se

176

01020304050051015202530354045500102030405005101520253035404550Ratio P' / GAxial Position [mm] 200 torr 60 A 200 torr 90 A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 200 torr 150 A 300 torr 150 A 400 torr 150 AFigure 4.26: Similar to Fig. 4.25 but for helium.

in Eq. (3.30) to the viscous heating term defined by Qv in Eq. (3.40). These two terms

(cid:32)

(cid:33)

appear in the heavy particle energy balance equation Eq. (3.29). Ratios of these two terms

Se
Qv

are shown in Figs. 4.31 and 4.32 for argon and helium respectively. These results are

once again from PLASIMO model calculations corresponding to a 6x6mm PW at various

operating conditions. These plots show that the electron heating term Se is everywhere and

for all conditions greater than the viscous heating term by at least an order of magnitude.

Thus it has been shown that in these conditions, viscosity does not play a significant role in

establishing the mass flow through the PW.

Concluding the comparisons in the single-radius systems between measurement and

PLASIMO model will be the flow rate. For the 6x6mm PW this can be seen in Fig. 3.10,

for both argon and helium at a variety of GCS pressures (different color/shape combina-

tions in the plot) and arc currents. In argon it can be seen that the modeled flow rate is

177

01020304050051015202530350102030405005101520253035Ratio P' / GAxial Position [mm] 200 torr 90A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 150 torr 150 A 200 torr 150 A 300 torr 150 A(cid:115)

Figure 4.27: The density factor

of various operating conditions in a 6x6mm PW.

n2
n(cid:48)
h

h

in argon plasma, determined via PLASIMO models

Figure 4.28: Similar to Fig. 4.27 but for helium.

178

0102030405001234567891001020304050012345678910Mass Flow Density Factor [1010 1/m]Axial Position [mm] 200 torr 60 A 200 torr 90 A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 200 torr 150 A 300 torr 150 A 400 torr 150 A0102030405002468101201020304050024681012Mass Flow Density Factor [1010 1/m]Axial Position [mm] 200 torr 90A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 150 torr 150 A 200 torr 150 A 300 torr 150 AFigure 4.29: The pressure drop factor
model of various operating conditions in a 6x6mm PW.

p in argon plasma, determined via PLASIMO

(cid:113)−P(cid:48)

Figure 4.30: Similar to Fig. 4.29 but for helium.

179

01020304050010020030040050060070080090010000102030405001002003004005006007008009001000Pressure Drop Factor [Pa/m]1/2Axial Position [mm] 200 torr 60 A 200 torr 90 A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 200 torr 150 A 300 torr 150 A 400 torr 150 A01020304050010020030040050060070080090010000102030405001002003004005006007008009001000Pressure Drop Factor [Pa/m]1/2Axial Position [mm] 200 torr 90A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 150 torr 150 A 200 torr 150 A 300 torr 150 AFigure 4.31: Ratio of electron collisional heating and viscous heating of the heavy particles
for a variety of PLASIMO modeled conditions.

Figure 4.32: Similar to Fig. 4.32 but for helium.

180

0102030405010100100001020304050101001000Ratio Se / QvAxial Position [mm] 200 torr 60 A 200 torr 90 A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 200 torr 150 A 300 torr 150 A 400 torr 150 A0102030405010100100001020304050101001000Ratio Se / QvAxial Position [mm] 200 torr 90A 200 torr 120 A 200 torr 150 A 200 torr 180 A 200 torr 210 AAxial Position [mm] 150 torr 150 A 200 torr 150 A 300 torr 150 Aslightly greater than the measured values, while the opposite is evident in helium. However it

should be noted that the behavior with respect to GCS pressure and arc current is generally

well-reproduced by the PLASIMO model.

Figure 4.33: Flow rates in the 6x6mm PW configuration for both argon (left) and helium
(right). Both measurements (solid points) and corresponding PLASIMO model values (open
points) are shown. The different colors represent different GCS pressure settings.

Flow rates in both a 6x6mm PW and a 8x6mm PW are shown in Fig. 4.34, and the

corresponding FRF values for these same configurations are shown in Fig. 4.35. Some of

these behaviors were seen previously in Fig. 4.1 but are examined for multiple different GCS

pressures here. In these figures, it can be seen that there is very little change in flow rate in

argon increasing PW length from 6 plates to 8 plates, and in fact the FRF is slightly lower

181

6090120150180210024681012141660901201501802100510152025303540455055Flow Rate [SLM]Current [A] 200 torr ( PLASIMO) 300 torr ( PLASIMO) 400 torr ( PLASIMO) 150 torr ( PLASIMO) 200 torr ( PLASIMO) 300 torr ( PLASIMO)Current [A]the 8x6mm configuration because the no-arc flow decreases when increasing the PW length

from 6 plates to 8 plates. In helium, however, there appears to be a slight increase in FRF

when the PW length is increased because, contrary to the behavior in argon, the flow rate

through the PW arc does decrease modestly when PW length increases from 6 to 8 plates.

Figure 4.34: Flow rate in a 6x6mm PW and 8x6mm PW at various GCS pressures and arc
currents in both argon and helium.

An alternative view of the FRF in Fig. 4.36 provides additional interesting information.

In this figure, FRF is plotted against what is called the retained arc power, which is the

difference of total arc power (calculated by taking the product of arc current and PW voltage

drop) and the total power cooled in all PW plates (determine via calorimetric analysis). This

182

60901201501802100510152025303540455055609012015018021005101520253035404550556x6mmFlow Rate [SLM]Current [A]Solid = ArgonCenter Cross = Helium 150 torr 200 torr 250 torr 300 torr 350 torr 400 torr8x6mmCurrent [A]Figure 4.35: Flow rate reduction (FRF) in a 6x6mm PW and 8x6mm PW at various GCS
pressures and arc currents in both argon and helium.

is the net amount of power available that could heat the plasma inside the PW channel. From

this, it can be seen that the power going into the helium arc can be viewed as less efficient at

higher GCS pressures than at lower ones, since as GCS pressure increases, it requires greater

retained arc power to attain some given FRF value. It is also very interesting to note that

in argon, the different GCS pressure curves have essentially converged to one line, whereas

this is not the case in helium.

183

6090120150180210024681012141618202224609012015018021081012141618206x6mmFlow Reduction FactorCurrent [A]Solid = ArgonCenter Cross = Helium 150 torr 200 torr 250 torr 300 torr 350 torr 400 torr8x6mmCurrent [A]Figure 4.36: Flow rate reduction (FRF) in a 6x6mm PW and 8x6mm PW at various GCS
pressures, plotted against retained arc power (rather than current as in Fig 4.35).

184

0246810120246810121416182022240246810120246810121416182022246x6mmFlow Reduction FactorRetained Arc Power [kW]Solid = ArgonCenter Cross = Helium 150 torr 200 torr 250 torr 300 torr 350 torr 400 torr8x6mmRetained Arc Power [kW]4.3 Two-Aperture Plasma Window Results

While the previous section focused on results for PW arrangements with a single aperture

size down the length of the channel, this section will focus on a narrower subset of results

from PW arrangements in which there are two different aperture sizes through the channel.
For example a 1x6mm 5x10mm PW is arranged: cathodes → one plate of 6 mm aperture →
five plates of 10 mm aperture → anode plate (the anode plate always has the same aperture

size as the plate immediately upstream of it). The notation for these PW configurations is

described in more detail in Section 2.1.2. These will hereafter be referred to as two-aperture

or two-radii PW configurations.

Some results of spectral calculations and comparisons with corresponding PLASIMO

values are shown in Fig. 4.37. This figure shows argon measurement and model comparisons

of electron density ne and temperature Te in both 1x6mm 5x10mm and 1x6mm 9x10mm PW

configurations with GCS pressure at 200 torr. The results are determined at the location of

plate 1 for both configurations. As in the single-radius configurations shown in the previous

section, there is decent agreement between measurement in model for much of the operating

conditions studied, with an obvious exception being that the electron temperature of low

current.

One possible reason for this lack of agreement at lower currents could be that at the

assumption of PLTE discussed in Section 2.2.3.1 may no longer be justified for the emissions

used, given that the electron density at these currents is below the threshold value for PLTE

existence.This can be seen in greater detail with Figs. 4.38 and 4.39. The former illustrates

electron density ne again in 1x6mm 5x10mm (left side of the figure) and 1x6mm 9x10mm

(right side of the figure) PW configurations in argon at plate 1, but this time for multiple GCS

185

Figure 4.37: Measured electron temperature (right) and density (left) values in both a
1x6mm 5x10mm and 1x6mm 9x10mm PW in argon with GCS pressure of 200 torr. Also
shown are corresponding PLASIMO model values. All properties are determined at the P1/6
or P1/10 position.

pressures (only measurements are shown, no PLASIMO results here). The latter is similar,

except that it pertains to electron temperature Te. We see from Fig. 4.38 that for the lower

current settings, the electron densities are too low to satisfy two of the three examined PLTE

criteria from Section 2.2.3.1, and for these the excitation temperature Texc determined via

the Boltzmann line method is likely diverged from the true electron temperature Te. Note

that the error bars in these figures do not reflect the applicability of PLTE or lack thereof.

Also of importance to examine in the two-radius system is the behavior of voltage drops

186

60901201501802101.01.11.21.31.41.51.61.71.81.92.02.12.22.36075901051201351501651801952100.00.20.40.60.81.01.21.41.61.82.0Electron Temperature [eV]Current [A] 1x6mm_5x10mm (Plate 1/10) PLASIMO 1x6mm_9x10mm  (Plate 1/6) PLASIMOElectron Density [1016 cm-3]Current [A]Figure 4.38:
Measured electron density at plate 1 in 1x6mm 5x10mm (left) and
1x6mm 9x10mm PW (right) PW configurations in argon for a variety of GCS pressures
and arc currents.

between components. We will see in Section 4.4.3 some dramatic consequences of the fact

the voltage drop from P1 (the 6 mm aperture plate) to P2 (the first 10 mm aperture plate)

in the two-radius systems examined is quite high. This can be seen in Fig. 4.40 for argon

(left) and helium (right). In these plots, GCS pressure is 200 torr, and the PW configuration

is 1x6mm 7x10mm. Note the change of ordinate scales between the argon and helium plots.

From this it is clear that the helium arc experiences some dramatically large voltage drops,

particularly across P1-P2. The region from cathodes-P1 encompasses the cathode fall region,

which is always relatively large so that gas ionizations can be initiated in the cathode vicinity

187

60901201501802100.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.960901201501802100.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.91x6mm_5x10mmElectron Density [1016 cm-3]Current [A] 150 torr 200 torr 250 torr 300 torr1x6mm_9x10mm 100 torr 150 torr 200 torrCurrent [A]Figure 4.39: Measured electron temperature at plate 1 in 1x6mm 5x10mm (left) and
1x6mm 9x10mm PW (right) PW configurations in argon for a variety of GCS pressures
and arc currents.

[28].

4.4 Lessons Learned and Potential Improvements

The lessons learned from the both the successes and shortcomings of the plasma window

system described in this thesis are something this author hopes will be leveraged for the next

generation of PW device. There is no shortage of challenges associated with implementing

the PW with a gas charge stripper, but based on the present research and past studies

188

60901201501802101.21.31.41.51.61.71.81.92.02.12.22.360901201501802101.21.31.41.51.61.71.81.92.02.12.22.31x6mm_5x10mmElectron Temperature [eV]Current [A] 150 torr 200 torr 250 torr 300 torr1x6mm_9x10mm 100 torr 150 torr 200 torrCurrent [A]Figure 4.40: Voltage drops between PW components in a 1x6mm 7x10mm PW for both
argon (left) and helium (right) arcs. For all cases, GCS pressure is 200 torr. Some of the
PW components between which a data point is taken are labeled on the left plot. Those
without labels are taken as between two adjacent plates, similar to the labeled P1-P2 point,
and though not indicated, the left plot points follow identical labelings.

by other groups, this author is confident that the PW with a gas charge stripper, or as a

means of isolating a gas target for any other application, is certainly possible. Though the

suite of potential improvements laid out in this section would result in improved capabilities

and performance, it is conceivable that not all can reasonably be implemented for a next

generation PW. In this section, it will be useful for the reader to recall the characteristics of

the PW and the test stand which were described in Section 2.1.

189

010203040506070024681012141618202224262830320102030405060700123456789101112131415HeliumAxial Position [mm]P8-AnodeP1-P2Between-Component Voltage Drop [V]Axial Position [mm] 90 A 120 A 132 A 150 A 180 A 210 AArgonCathodes-P14.4.1 Cathode Structure

Discussion and conclusions about considerations for cathode usage in the PW were presented

in Section 2.3, primarily by conducting a survey of existing literature on thermionic cathode

usage with particular attention to thoriated and lanthanated tungsten studies in argon and

helium arcs. A recap will be given here on some those conclusions and how they can be

leveraged.

Recommendation Topic 1:

It is expected that the cathode lifetime scales with the current density emitted. It there-

fore would be beneficial in terms of supporting longer lifetimes to have a greater combined

cathode emitting surface than presently in the PW. For example, the current setup with 3

thoriated tungsten cathodes could be changed to allow 6, or possibly more. Alternatively, a

knife-edge ring cathode of thoriated tungsten is another option that could be explored since

it offers a large emitting surface area. It is unclear how stable this arrangement would be,

since emission tends to occur from a localized spot on the cathode. This arc attachment and

the immediate vicinity have their morphologies changed with operating time, as discussed in

Section 2.3, and may migrate to different zones if the WF-lowering-dopant composition near

the initial cathode spot becomes less favorable for emission. In this sense it would possibly

be beneficial having the relatively large surface area of the ring-like cathode.

Recommendation Topic 2:

In some instances it appears that the copper shields into which the thoriated tungsten

cathode needles are inserted (see Fig. 2.8) can be deformed by the local plasma. An example

of this is shown in Fig. 4.41. Sometimes it even appears that this copper shield, or the water-

cooled copper cathode holder into which the shield threads, as is also illustrated in Fig. 4.41

190

with the label of possible emission site. It is therefore suggested that any copper holding

component of the cathodes be positioned farther from the arc axis by using longer cathodes.

As suggested in Ref. [93], a longer cathode would have the added benefit of promoting

greater diffusion of thoria (if this is thoriated tungsten) in the cathode and extending its

usable lifetime.

Recommendation Topic 3:

Due to there being several channel diameter changes in the vicinity of the cathodes with

the present PW setup (entrance of cathode housing is 10 mm diameter, then it opens to

13 mm where the cathodes are inserted to the channel, then constricts down to the 6 or 10

mm diameter of the first PW plate), as well as the cathodes themselves positioned inside

the gas flow, there may be a large degree of turbulence and swirl. As reported in Ref. [96],

this swirl can contribute to substantially enhanced erosion time. One thing at the very least

which could be done to help alleviate this would be to have a uniform channel diameter in

the cathode vicinity.

4.4.2 Plasma Window Structure

Recommendation Topic 1:

Cracked or otherwise damaged o-rings are presently a frequent occurrence which results in

air leaks. These leaks are highly problematic near cathodes in particular, since as discussed

in Section 2.3 the presence of oxygen can decrease cathode lifetimes. This also would be

a significant issue if in recirculation mode due to the gas impurity continuously building

up. The recirculation mode would be absolutely necessary for operation with a gas charge

stripper, so a redesign of the cathode plate and between-plate components shown in Fig.

2.6. One possibility for why the o-rings become damaged is that the plates at the part in

191

Figure 4.41: Photos of cathodes and their holders after attempting an arc in helium PW
of 6x10mm configuration, which ultimately proved too unstable for data collection. The
copper shield has been deformed and just below on the left photo there is an indentation in
the copper holder, possibly due to this acting as an emission site.

192

contact with the o-rings become hot during the PW operation and so can cause thermal

contact damage, as could the inner alumina insulator which is also in contact with the o-

ring. Furthermore, when the plates are hot they thermally expand and therefore squeeze

the o-rings even more. The frequent observation of o-ring damage could be attributed to

this combination of factors. To address this, it is suggested that the plates be made radially

larger to provide more space for these components. The o-ring could then be of a larger

diameter, so that it is beyond radially beyond where the coolant loop (recall positioning of

these plate features in Fig. 2.6) is inside the plate, so that it would be less likely to suffer

any thermal contact damage from the plates. Additionally, one could leave a small space

between this o-ring and the inner insulator to limit thermal contact damage from that as

well (so there would be a gap between components B. and C. in the figure). Lastly, with a

larger-radius plate, one could even place a redundant o-ring beyond the outer FR4 insulator

(component A. in the figure) in case of failure of the inner.

Recommendation Topic 2:

It was noted that after long operation times, an accumulation of copper would often

appear on the plasma-facing insulators between the plates, which because this primarily

occurs on the cathode-side of the PW, presumably is a result of deposition of small amounts

of copper removed from the copper cathode shields. this copper deposition often resulted in

a conductive bridge between two plates on the cathode-side of the PW, effectively shorting

the plates together. This is undesirable as it would result in a greater voltage drop between

other plates, such that the total PW voltage drop remained relatively unchanged. As will

be explained later, having excessive plate-to-plate voltage drops can be problematic. One

potential solution to this issue of conductive bridging building up across the inter-plate

insulators is to introduce a different plasma-facing shape for them, such as those illustrated

193

Figure 4.42: A pictorial representation of the undesired copper bridging effect that often
occurs for cathode-side plates. Also shown are different possible insulator designs that may
inhibit the copper bridging effect.

in Fig 4.42.

Recommendation Topic 3:

Though it shows promise for meeting the requirements of large-aperture while still having

substantial flow-reduction capabilities (see Figs. 4.1 and 4.2), the PW configurations of

1x6mm Nx10mm do have more issues than in a single-radius configuration which must be

addressed for a next generation PW. The principal concern is related to the part of the

channel which expands from 6 mm aperture plate to the first 10 mm aperture plate. Across

these two plates there is always a relatively large voltage drop, greater that between any

two adjacent plates elsewhere in the PW. As a result, ions within the expansion region feel

a strong electric field backwards towards the exposed surface (on the anode-side) of the 6

mm aperture plate. For higher currents in particular, this can result in catastrophic removal

of the exposed copper plate. This removed copper material was subsequently redeposited

194

Left: A photo of dramatic and rapid copper removal

Figure 4.43:
from P1 in a
1x6mm 9x10mm PW operated in helium at 300 torr GCS pressure, 210 A arc current.
Middle: The remove material was redeposited along the channel wall downstream of the
removal site. Right: The result of continued copper surface removal, which has here cut
through to the water coolant path, resulting in even more extensive damage.

along the PW channel walls, rapidly causing the bridging effect between plates discussed

previously. This can be seen in Fig. 4.43. The left and center photos were taken after

operating a 1x6mm 9x10mm PW in helium at 300 torr GCS pressure, 210 A arc current

over a period of 100 minutes, and the right photo taken after operating a 1x6mm 7x10mm

PW in helium at 300 torr GCS pressure, 180 A arc current over a period of about 18 hours

(recall what the un-damaged plate surface looks like from Fig. 2.6). The voltage drop

between P1 and P2 in the first case was about 30 V and in the second case was 24 V, which

as was discussed in Section 4.3 and Fig. 4.40, is a characteristic of the expansion part of the

two-radius PW configurations. Although this is a catastrophic problem, there are fortunately

several possible steps that can be taken to reduce its likelihood.

Firstly, note from Fig. 4.43 that the copper material removal occurs on the part of the

plate which is unprotected by the alumina insulator. As a result, one would expect that if

195

this insulator had an inner diameter of 6 mm to match that of P1, the plate would not suffer

such damage. Secondly, so long as the PW overall geometry is preserved, changes to plate

count don’t impact the the total PW voltage drop. As a result, the voltage drop between any

two plates will be reduced if the total plate count is increased (again assuming PW overall

geometry is unchanged), so having a larger number of plates would mean the drop between

the 6 mm aperture plate and the first 10 mm aperture plate is decreased, so less energetic

ion-plate collisions. Lastly, one could have a more gradual stepping from the 6 mm aperture

to 10 mm aperture, e.g. having in between a plate of 8 mm aperture.

In addition to the above recommendations hopefully reducing the likelihood of the type of

damage observed in Fig. 4.43, it’s highly desirable to have an early detection of the problem,

as well as appropriate interlocks to ensure that if it develops, the arc is automatically shut off

to prevent further damage. The power supply voltage data can be continuously observed for

any unexpected behaviors which may provide information that the arc is behaving unstably

or destructively.

4.4.3 Recirculation

Recommendation Topic 1:

Recirculation of the gas that flows through the GCS and PW is an essential capability

for long-term operation of the PW, particularly if the desired gas is helium, since simply

expelling the gas to atmosphere is obviously expensive and wasteful. One success from this

PW research was a 6-day continuously operated trial in recirculated helium, with the original

GCS pressure set to 300 torr and arc current of 180 A, in a 1x6mm 7x10mm PW. It should

be noted that this is the same type of PW configuration and similar operating conditions

which generated the severe damage shown in Fig. 4.43, and while this long-duration trial

196

Figure 4.44: The three thoriated tungsten cathodes after a 6-day continuous operation run
in helium at GCS pressure 300 torr and 180 A arc current. Also shown for comparison is an
unused cathode.

did not result in such damage, an air leak did develop, causing a continuous accumulation of

oxygen and nitrogen impurities which were observed in the continuous collection of spectra

using the spectrometer described in Section 2.1.3.1. Air leaks such as this, as mentioned

above, are particularly essential to prevent for recirculation as the impurities will build up

continuously. As mentioned in Ref. [23], even small amounts of impurities can impede the

charge stripping capabilities of helium.

After this run, the cathodes were examined to gauge their state after such long-duration

operation. These are shown in Fig. 4.44 and it is clear they were substantially deformed

over the course of operation. Ultimately the arc collapsed of its own accord, which is a still

common occurrence in helium PW arc, and a highly uncommon one in the argon arc. In fact,

this instability in the helium arc not only made data acquisition challenging, but but would

certainly preclude the PW from reliably operating for long durations, and it is absolutely

necessary that such instabilities be addressed if a future generation PW were to be used with

a helium charge stripper in an ion beam. Unfortunately, the root cause(s) of this instability

could not be conclusively ascertained in the work of this thesis, but it is likely attributed to

197

sub-optimum cathode properties and the ensuing insufficient ionization of background gas

to maintain the arc over its length. Towards this end, it is particularly crucial for a next

generation PW to consider the possible improvements laid out above regarding cathodes and

their usage. One thing that became clear however, is that the likelihood of this instability

which can cause the helium PW arc to collapse increases at higher GCS pressures and at

lower arc currents. To summarize, while this 6-day helium run was a successful step towards

the PW being capable of isolating a GCS continuously over a long duration, shortcomings

such as air leaks and cathode deformations must be addressed to ensure the desired stripping

gas is maintained and the PW can operate continuously for a longer period.

Recommendation Topic 2:

When changing PW gas from argon to helium, Ar II emissions are observed to linger for

some time after the argon feed has been closed and the flow has been transitioned to helium

(the process is first described in Section 2.1.2). It is likely that some argon remains trapped

near the cathode as a result of it having a much lower ionization energy than helium, so

is more easily ionized in the vicinity of the cathodes, and then these ions fall through the

cathode potential drop before recombining and being ionized again to repeat the cycle. The

net result is a much slower depletion of the argon than would be expected. Figure 4.45

illustrates an example of this by looking at several emission peaks immediately following the

transition from argon to helium flow for a 6x6mm PW with GCS pressure 200 torr and arc

current 120 A. In this it can be seen that even after 3 minutes of operating in nominally pure

helium, some Ar II peaks remain. It can also be seen that this is particularly problematic

when attempting to determine plasma properties with the spectral acquisitions because the

Ar II lines are substantially more intense than the helium ones. This is still in the fresh gas

mode where the gas is expelled to atmosphere rather than recirculated.

198

Figure 4.45:
Spectral acquisitions at several different times, of two narrow wavelength
windows. The Ar II emissions can clearly be seen to persist for several minutes after switching
from argon to helium gas. This data was taken in fresh gas (expelled to atmosphere), not
recirculation.

199

434.0434.5435.0435.5436.005101520253035446.5447.0447.5448.0448.50123456Ar II 435.2 nm lineIrradiance [a.u.]Wavelength [nm] t = 0 min t = 0.12 min t = 3.5 minAr II 434.8 nm lineHe I 447.1 nm lineAr II 448.2 nm lineWavelength [nm]It is therefore recommended that the PW is operated in fresh gas for at least 20-30

minutes prior to recirculating, otherwise this argon gas will remain trapped with the helium.

It’s also possible that different operating conditions could help flush out the argon more so

than others, though this possibility was not thoroughly explored in the presently-discussed

research.

4.4.4 Plasma Window Performance Summary

As has been mentioned, to utilize the plasma window with a gas charge stripper, it is

desirable to have as great a pressure as attainable with as low of a flow rate as possible,

which is achieved by having a large arc current. Higher pressure and higher current both

result in larger power deposition. A sizeable amount of this power is deposited into the

cascaded plates enclosing the arc, and the remainder is deposited into the heat shielding

cone structure within the expansion chamber and the expansion chamber walls themselves

(these components are described in Section 2.1.2).

To provide an idea of what to expect for a power deposition from the arc for a next

generation PW, Figs. 4.46 - 4.50 show the PW arc power in both argon and helium for the

PW configurations studied in this work. Note that this is only the arc power, and other

sources of power associated with operation of the PW include the power dissipated through

the resistors described in Section 2.1.2 as well as the wall power of the vacuum pumps. The

coolant system must be capable of managing at least the sum of all these powers. Using

the same calorimetric technique described in Section 2.1.3.2, the system of vacuum pumps

require about 5 kW of cooling power, while the power dissipated through the 1 Ohm resistors

schematically shown in Fig. 2.11 is of course current-dependant, calculated as P = I2R. All

told, when the PW is operating with GCS at 300 torr or above (300 torr being a modest target

200

Figure 4.46: Arc power for various arc currents GCS pressures in the PW configuration of
6x6mm.

Figure 4.47: Arc power for various arc currents GCS pressures in the PW configuration of
8x6mm.

201

6090120150180210024681012141618206090120150180210024681012141618206x6mmArc Power [kW]Current [A] 150 torr 200 torr 250 torr 300 torr 350 torr 400 torrArgonHeliumCurrent [A]609012015018021002468101214161820222460901201501802100246810121416182022248x6mmPW PowerCurrent [A] 150 torr 200 torr 250 torr 300 torrArgonHeliumCurrent [A]Figure 4.48: Arc power for various arc currents GCS pressures in the PW configuration of
1x6mm˙7x10mm.

value for utilizing this on an ion beam), at 150 A or above, the overall power consumption

in helium can easily exceed 40 kW (in argon for all else equal, it’s somewhat lower), and

the coolant supply MUST be able to cope with at least this amount of power, especially for

when the system is to be operated continuously for a two-week period.

4.4.5 Charge Stripper Gas Species Choice

Here will be provided a set of pros and cons for choosing either argon or helium as a possible

charge stripping gas for an ion beam.

Equilibrium Charge State

Studies on the equilibrium charge state of heavy ion beams being stripped by gases have

been carried out in e.g. Refs. [2, 22, 23, 31]. In these studies, specifically for an incoming

ion beam of 238U35+ at 11 MeV/nuc, it was found that the equilibrium charge state (post-

202

6090120150180210024681012141618609012015018021002468101214161820222426281x6mm_7x10mmArc Power [kW]Current [A] 100 torr 150 torr 200 torr 250 torr 300 torrArgonHeliumCurrent [A]Figure 4.49: Arc power for various arc currents GCS pressures in the PW configuration of
1x6mm˙9x10mm.

Figure 4.50: Arc power for various arc currents GCS pressures for two the PW configurations,
both of which are for argon arc. The left plot is for 6x10mm configuration and the right plot
is for 1x6mm˙5x10mm.

203

6090120150180210024681012146090120150180210024681012141618202224262830321x6mm_9x10mmArc Power [kW]Current [A] 100 torr 150 torr 200 torr 250 torr 300 torr % (4) % (5)ArgonHeliumCurrent [A]60901201501802100123456789101112136090120150180210012345678910111213 150 torr 200 torr 250 torr 300 torr6x10mmArc Power [kW]Current [A]Argon1x6mm_5x10mmCurrent [A]Argonstripping) in helium gas was 66+ and in argon gas was 56.6+ which were compared to the

equilibrium charge state through a solid carbon foil of 72+. So, helium tends to provide

higher charge states as a stripping gas of heavy ions such as uranium.

Stability

As has been discussed both in Section 2.3 and Section 4.4.3, the helium arc frequently

suffers from instability which can cause the arc to collapse entirely. When this happens,

GCS pressure drops precipitously because it no longer has the flow rate reduction of the arc,

so the instability in the helium arc absolutely must be addressed for the PW to be useful

with a helium charge stripper. The root cause(s) and potential solutions of this instability

remain somewhat elusive but it is likely that it originates at the cathode side, perhaps as

a momentary repositioning of the arc spot on the cathode surface. Alternative cathode

designs described in Section 4.4.2 could possibly reduce the frequency of this happening and

therefore increase stability. The argon arc did not seem to suffer such instability, likely partly

attributed to it having a much lower ionization degree, so any arc attachment repositioning

that happens doesn’t suppress the production of ions and electrons from gas that sustains

the arc.

Lifetime

On the topic of cathode lifetime, it is not as yet known how the long term performance

of thoriated tungsten cathodes in argon compares with that in helium. A thorough study

on the long term performance of these cathodes should be the next topic of investigation

related to the PW in the context of a gas charge stripper.

Flow Rate and Flow Reduction Factor

The figures which convey flow rate and flow reduction factors (FRF) in various operating

conditions and geometries are Figs 4.34, 4.35, 4.1, and 4.2. From these figures we see that for

204

equal GCS pressure and arc current, argon exhibits substantially lower flow rate and greater

FRF than those in helium.

Arc Power

As seen in Figs. 4.46 - 4.50, the arc power into the argon arc is substantially less than that

into the helium arc, at equivalent GCS pressure and arc currents. Ultimately the entirety

of this power must be cooled, in addition to the other components not directly part of the

arc but still require cooling, such as the pumps and resistors, as mentioned in Section 2.1.2

The results in these figures can be used as a guide for a future PW to assess what amount

of cooling power will need to be provided throughout the PW region.

4.5 Empirical Scaling Behaviors

One goal of this project was to attempt to determine the scaling behavior of flow rate as a

function of the various controllable parameters of arc current, GCS pressure, geometry, and

gas species. Examining each scaling independently ultimately allowed an overall empirical

scaling relation to be obtained, such that the flow rate is linearly related to an overall

empirical scaling function (denoted ESF ). This is presented in Fig. 4.51, for argon and

helium separately. This empirical scale function ESF is defined as:

where ¯Y is calculated if there is a two-radius (or more) PW channel as:

ESF ∝ P 5/3
I2/3 ¯Y 2

,

(cid:80) L
(cid:80) L

¯Y =

(4.5)

(4.6)

1/2
i
1/4
i

/D4
i
/D2
i

,

205

Figure 4.51: An empirical scaling relationship between operating conditions and flow rate.
Each PW configuration shown includes the multitude of operating conditions explored within
that configuration.

in which the subscript i denotes the channel portion, which has its own length L and diameter

D, both in units of mm here. The pressure P is the GCS pressure and is here in units of

torr and the arc current I is in units of amps. The relationship is plotted across a multitude

of operating conditions (varied pressures and currents).

It should be stressed that this

relationship is phenomenological, and there may be finer adjustments to the powers of the

properties to bring about a collectively better fit to a straight line. This is particularly true

for the geometric factor ¯Y .

206

0.01.53.04.56.00246810121416182022242628303234360.000.751.502.253.000102030405060708090100110120 6x6mm Plates (Config. A) 8x6mm Plates (B) 1x6mm_5x10mm Plates (D) 1x6mm_7x10mm Plates (E) 1x6mm_9x10mm Plates (F) 6x10mm Plates (G)Flow Rate [SLM]ArgonHeliumEmpirical Scale Function 105 [torr5/3 mm7/2 / A2/3]  It is worth mentioning that there likely are several caveats to the utilization of this

scaling law to consider before treating it as a universal scaling relation. In the PW, an areal

expansion just downstream of the anode results in a choked flow condition. We know this

because of a simple test in which the booster pump was turned off during PW arc operation,

resulting in a pressure rise of the expansion chamber downstream of the PW, but crucially did

not impact any pressure, flow, or other plasma properties within the PW channel itself. The

only explanation is the establishment of a choked flow condition at the expansion location

after the PW. Thus we consider a requirement to use the scaling law of Eq. (4.5) and Fig.

4.51 is that there exists a choked flow condition, i.e. the pumping speed is sufficiently great.

207

Chapter 5

Conclusions

As heavy ion accelerator facilities push for greater beam intensity with greater beam particle

count, the solid charge strippers that have traditionally been used to remove further electrons

from the ion beam are less viable options due to their short lifetimes at such intensities. In

light of this, an alternative in the form of a gas charge stripper (GCS) is a promising avenue,

but is challenging to implement because it requires a large pressure and aperture, yet also

necessary is a low gas leakage rate from the GCS to the surrounding beamline. The plasma

window (PW) is a device which can meet these challenges by substantially reducing that gas

leakage rate, all else being equal.

Flow Reduction Mechanisms

One goal of this study was to ascertain what characteristics about the plasma most

contribute to the observed flow rate reduction. A detailed characterization of the plasma

within was carried out, particularly for the focused case of a 6x6mm PW configuration (6

plates, each of 6 mm aperture). In this PW configuration, the flow rate could be reduced by

up to a factor of 24 in argon and 15 in helium from what it would be without the presence

of the arc.

A 2D PW arc model was developed using PLASIMO and used to investigate an array of

plasma properties and compare to measurements, in an effort to assess if this tool would be

useful in gaining further insight into the flow reduction mechanisms, as well as in predicting

208

and understanding the behavior of the next generation plasma window. While the models

generally produced results that matched reasonably well with experimental ones, one must

start off with a clear idea of what the cathode-side and anode-side pressures are to use

as boundary conditions. This can be more easily done in a single-radius PW such as the

6x6mm configuration studied in this work, by extrapolating from the pressure measurements

obtained and presented in this thesis in Fig. 3.8. A two-radius (or more) PW such as

the 1x6mm 5x10mm configuration further requires input of the voltages at the positions of

cathodes, the expansion location, and anode. However, one issue with using this modelling

software for these two-radius systems is that it cannot treat the total arc current as a constant

value over the channel, so the 6 mm and 10 mm aperture portions can have non-identical

currents, which doesn’t conform to the reality of the PW.

An expression that indicates for mass flow was obtained in Section 3.3, and an examina-

tion into which properties most heavily influence it was conducted. In Section 4.2.6 it was

shown by thorough examination of PLASIMO modeled properties that what has most often

been cited as the flow-limiting attribute of the PW, the large viscosity that it generates, is

(cid:115)
− n(cid:48)

h
n2
h

indeed not a substantial factor. Far more important is a heavy density factor,

which

the mass flow is proportional to. For a given plasma pressure Pp, the heavy particle density

nh is reduced with increasing electron density ne, electron temperature Te, heavy particle
(gas and ion) temperature Th, and heavy particle axial rate of change n(cid:48)

h. Greater presence

of electrons means they more rapidly heat the gas. As a result, all of the parameters men-

tioned above increase with increasing arc current, matching the observation that measured

flow rates are lower for higher arc currents. The conclusion is that what is most important in

establishing the flow rate reduction is substantial ionization of the flowing gas which enables

greater and quicker heating.

209

Plasma Window Outlook

Although the PW was successfully operated in helium for 6 days under continuous gas

recirculation, there is still much room for improvement. Some considerations and recom-

mendations were summarized in Section 4.4. Employing at least some of these should help

PW maintain better stability, lifetime, or both. In the same section, many other potential

improvements to the PW system are also presented, and this author strongly recommends

at least some of these features be implemented for a next generation PW for isolating a high

pressure gas target. The long-term behavior of the cathodes in both argon and helium in

particular demands further study, as does the impact of the shape of the cathode(s) used

since it is likely alternative designs to the three needle-cathode arrangement used in this

thesis could reduce the surface current density and extend operating lifetime.

A number of conclusions have been reached regarding considerations in optimizing the

PW geometry for the purpose of gas charge stripping of ion beams. Based on the results

described in this thesis, it is recommended that a next generation PW employ a plate config-

uration akin to a 2-radius PW (e.g. the 1x6mm 5x10mm configuration) because this provides

both a modest flow reduction degree (between that of a 6x6mm and a 6x10mm configura-

tion), but also is composed of a wide aperture channel - with the exception of the single 6 mm

aperture cathode-side plate - to permit un-scraped beam passage. Additionally, it was found

that extending the overall arc length (e.g. the 6x6mm configuration to 8x6mm configuration)

confers a slightly further flow rate reduction, and does so at the expense of a greater arc

power which must be cooled. To help provide some ability to predict the flow rate through

the PW for some desired operating conditions (GCS pressure, arc current, gas species, and

PW geometry), an empirical scaling relation was developed. This was demonstrated in Fig.

4.51.

210

While helium can afford higher equilibrium charge states for the outgoing ion beam, it

is generally far more difficult to maintain. For equivalent GCS pressure and arc current,

compared to with argon, for helium the gas flow rate escaping from the GCS is significantly

higher, the power deposition is much greater, and it suffers from greater arc instability and

thus more prone to unexpected and undesired shutoffs.

It is not clear which gas would

experience the greater lifetime of the thoriated tungsten needle cathodes. In order to make

use of the plasma window with a gas charge stripper, there must be more investigation into

the root causes and possible solutions to the helium arc instability, as well as the likely

related problem of the cathode lifetime. Previous studies (mentioned in Section 2.3) have

successfully operated in argon gas for up to 1500 hours thoriated tungsten cathodes, the

same as those used in this thesis, though in this current work, nowhere near that operating

duration was observed. Furthermore, to this author’s knowledge there have been no such

studies for very long term cathode operation in a helium arc. It is likely that in order to

achieve the desired longevity of two weeks continuous operation for a heavy ion accelerator

facility, a different cathode structure would be necessary. Some alternatives to the three-

needles structure used in the present work were laid out in Section 4.4.2. Testing such

alternative cathode structures should be another next step to take in studying the plasma

window in the context of a gas charge stripper. It is this author’s belief that the goal of a

two week uninterrupted and stable operation of the plasma window is attainable provided

some attention is given to the challenges mentioned above,and the suggested design changes

are implemented. In general, the plasma window is a promising device with the capability

of greatly benefiting a gas charge stripper system for future high intensity ion accelerators.

211

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